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Deck 5: Rational Functions and Conics
Full screen (f)
Question
Determine the equations of any horizontal and vertical asymptotes of 
.
A) horizontal:
; vertical: 
B) horizontal:
; vertical: 
C) horizontal:
; vertical: 
D) horizontal:
; vertical: 
E) horizontal:
; vertical: none
.A) horizontal:
; vertical: B) horizontal:
; vertical: C) horizontal:
; vertical: D) horizontal:
; vertical: E) horizontal:
; vertical: none
Question
Given 
:
a. Determine the domains of
.
b. Simplify
and find any vertical asymptotes.
c. Complete the table.
d. Explain how the two functions differ.
:a. Determine the domains of
.b. Simplify
and find any vertical asymptotes.c. Complete the table.
d. Explain how the two functions differ.
Question
Given 
:
a. Determine the domains of
.
b. Simplify
and find any vertical asymptotes.
c. Complete the table.
d. Explain how the two functions differ.
:a. Determine the domains of
.b. Simplify
and find any vertical asymptotes.c. Complete the table.
d. Explain how the two functions differ.
Question
Find the domain of 
.
A) all real numbers except
B) all real numbers except
C) all real numbers except
D) all real numbers except
E) all real numbers
.A) all real numbers except
B) all real numbers except
C) all real numbers except
D) all real numbers except
E) all real numbers
Question
Find the domain of 
.
A) all real numbers
B) all real numbers except
C) all real numbers except
D) all real numbers except
E) all real numbers except
.A) all real numbers
B) all real numbers except
C) all real numbers except
D) all real numbers except
E) all real numbers except
Question
Determine the equations of any horizontal and vertical asymptotes of 
.
A) horizontal: none; vertical: none
B) horizontal:
; vertical: 
C) horizontal:
; vertical: 
D) horizontal:
; vertical: 
E) horizontal:
; vertical: 
.A) horizontal: none; vertical: none
B) horizontal:
; vertical: C) horizontal:
; vertical: D) horizontal:
; vertical: E) horizontal:
; vertical: Question
Determine the zeros (if any) of the rational function 
.
A)
B) no zeros
C)
D)
E)
.A)
B) no zeros
C)
D)
E)
Question
Determine the zeros (if any) of the rational function 
.
A)
B) no zeros
C)
D)
E)
.A)
B) no zeros
C)
D)
E)
Question
Determine the equations of the vertical and horizontal asymptotes of the graph of the function 
.
A) horizontal:
; vertical: 
B) horizontal:
; vertical: 
C) horizontal:
; vertical: 
D) horizontal:
; vertical: 
E) horizontal:
; vertical: 
.A) horizontal:
; vertical: B) horizontal:
; vertical: C) horizontal:
; vertical: D) horizontal:
; vertical: E) horizontal:
; vertical: Question
Determine the equations of any horizontal and vertical asymptotes of 
.
A) horizontal:
; vertical: 
B) horizontal:
; vertical: none
C) horizontal:
; vertical: 
D) horizontal: none; vertical: none
E) horizontal:
; vertical: none
.A) horizontal:
; vertical: B) horizontal:
; vertical: noneC) horizontal:
; vertical: D) horizontal: none; vertical: none
E) horizontal:
; vertical: none Question
Given 
:
a. Determine the domains of
.
b. Simplify
and find any vertical asymptotes.
c. Complete the table.
d. Explain how the two functions differ.
:a. Determine the domains of
.b. Simplify
and find any vertical asymptotes.c. Complete the table.
d. Explain how the two functions differ. Question
Determine the zeros (if any) of the rational function 
.
A)
B)
C)
D)
E) no zeros
.A)
B)
C)
D)
E) no zeros
Question
The graph of the function 
is shown below. Determine the vertical and horizontal asymptotes of its graph. 
A) horizontal:
B) horizontal:
C) horizontal:
D) horizontal:
E) horizontal:
is shown below. Determine the vertical and horizontal asymptotes of its graph. A) horizontal:
B) horizontal:
C) horizontal:
D) horizontal:
E) horizontal:
Question
Determine the equations of any horizontal and vertical asymptotes of 
.
A) horizontal:
; vertical: 
B) horizontal:
; vertical: 
C) horizontal:
; vertical: none
D) horizontal:
; vertical: 
E) horizontal:
; vertical: 
.A) horizontal:
; vertical: B) horizontal:
; vertical: C) horizontal:
; vertical: noneD) horizontal:
; vertical: E) horizontal:
; vertical: Question
The graph of the function 
is shown below. Determine the domain. 
A)
B)
C)
D)
E)
is shown below. Determine the domain. A)
B)
C)
D)
E)
Question
Determine the domain of 
.
A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
.A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
Question
Determine the domain of 
.
A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
.A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
Question
Which of the following is the graph of the given equation? 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the domain of 
.
A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
.A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
Question
Determine the domain of the function 
.
A) Domain: all real numbers except
B) Domain: all real numbers except
C) Domain: all real numbers except
D) Domain: all real numbers except
E) Domain: all real numbers
.A) Domain: all real numbers except
B) Domain: all real numbers except
C) Domain: all real numbers except
D) Domain: all real numbers except
E) Domain: all real numbers
Question
Given 
:
a. Determine the domains of
.
b. Simplify
and find any vertical asymptotes.
c. Complete the table.
d. Explain why a graphing utility may not show the difference in the domains of f and g.
:a. Determine the domains of
.b. Simplify
and find any vertical asymptotes.c. Complete the table.
d. Explain why a graphing utility may not show the difference in the domains of f and g.
Question
A 1500-liter tank contains 30 liters of a 10% acid solution. You add x liters of a 90% acid solution to the tank. Determine a function C that represents the proportion of acid to the total solution in the final mixture.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Determine the equations of any horizontal and vertical asymptotes of 
.
A) horizontal: none; vertical: none
B) horizontal:
; vertical: 
C) horizontal:
; vertical: 
D) horizontal:
; vertical: 
E) horizontal:
; vertical: 
.A) horizontal: none; vertical: none
B) horizontal:
; vertical: C) horizontal:
; vertical: D) horizontal:
; vertical: E) horizontal:
; vertical: Question
Find the vertex and focus of the parabola. 
A) vertex: (0, 0) focus:
B) vertex:
focus: 
C) vertex: (0, 0) focus:
D) vertex:
focus: 
E) vertex: (0, 0) focus:
A) vertex: (0, 0) focus:
B) vertex:
focus: C) vertex: (0, 0) focus:
D) vertex:
focus: E) vertex: (0, 0) focus:
Question
Find the vertex and focus of the parabola. 
A) vertex: (0, 0) focus:
B) vertex:
focus: (0, 0)
C) vertex: (0, 0) focus:
D) vertex: (0, 0) focus:
E) vertex:
focus: (0, 0)
A) vertex: (0, 0) focus:
B) vertex:
focus: (0, 0)C) vertex: (0, 0) focus:
D) vertex: (0, 0) focus:
E) vertex:
focus: (0, 0) Question
Question
Given 
, determine the equations of any slant and vertical asymptote.
A) slant: none; vertical: none
B) slant:
; vertical: 
C) slant:
; vertical: 
D) slant:
; vertical: none
E) slant:
; vertical: 
, determine the equations of any slant and vertical asymptote.A) slant: none; vertical: none
B) slant:
; vertical: C) slant:
; vertical: D) slant:
; vertical: noneE) slant:
; vertical: Question
Given 
, determine the equations of any slant and vertical asymptote.
A) slant:
; vertical: 
B) slant:
; vertical: 
C) slant:
; vertical: 
D) slant:
; vertical: 
E) slant:
; vertical: 
, determine the equations of any slant and vertical asymptote.A) slant:
; vertical: B) slant:
; vertical: C) slant:
; vertical: D) slant:
; vertical: E) slant:
; vertical: Question
Solve for any x-intercepts for the graph of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Question
Solve for any x-intercepts for the graph of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Determine the domain of the function 
.
A) Domain: all real numbers
B) Domain: all real numbers except
C) Domain: all real numbers except
D) Domain: all real numbers except
E) Domain: all real numbers except
.A) Domain: all real numbers
B) Domain: all real numbers except
C) Domain: all real numbers except
D) Domain: all real numbers except
E) Domain: all real numbers except
Question
Given the rational function 
:
a. Using a graphing utility, sketch the graph in the given window frame:
b. Determine the domain of the function.
c. Identify any vertical asymptotes.
d. Determine the equation of the slant asymptote.
:a. Using a graphing utility, sketch the graph in the given window frame:
b. Determine the domain of the function.c. Identify any vertical asymptotes.
d. Determine the equation of the slant asymptote.
Question
Find the standard form of the equation of the parabola and determine the coordinates of the focus. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Match the equation with its graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
A 1500-liter tank contains 70 liters of a 30% acid solution and you add x liters of a 70% acid solution to the tank. If the function C, which represents the proportion of acid to the total solution in the final mixture, is given by 
, what percent does the concentration of acid appear to be approaching as x increases without bound? (Ignore the physical constraint that 
.)
A) 100%
B) 30%
C) 40%
D) 70%
E) 20%
, what percent does the concentration of acid appear to be approaching as x increases without bound? (Ignore the physical constraint that .)A) 100%
B) 30%
C) 40%
D) 70%
E) 20%
Question
Solve for any x-intercepts for the graph of 
.
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
Question
Determine the domain of 
.
A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
.A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
Question
A 1500-liter tank contains 70 liters of a 30% acid solution and you add x liters of a 70% acid solution to the tank. If the function C, which represents the proportion of acid to the total solution in the final mixture, is given by 
, determine the domain based upon the physical constraints of the problem.
A)
B)
C)
D)
E)
, determine the domain based upon the physical constraints of the problem.A)
B)
C)
D)
E)
Question
Given 
:
a. Determine the domains of
.
b. Simplify
and find any vertical asymptotes.
c. Complete the table.
d. Explain how the two functions differ.
:a. Determine the domains of
.b. Simplify
and find any vertical asymptotes.c. Complete the table.
d. Explain how the two functions differ.
Question
Find the standard form of the equation of the ellipse with the following graph. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Identify the center and radius of the circle. 
A) center: (-6, 0) radius: 7
B) center: (0, -6) radius: 49
C) center: (0, 6) radius: 49
D) center: (0, -6) radius: 7
E) center: (6, 0) radius: 7
A) center: (-6, 0) radius: 7
B) center: (0, -6) radius: 49
C) center: (0, 6) radius: 49
D) center: (0, -6) radius: 7
E) center: (6, 0) radius: 7
Question
Find the vertex and focus of the parabola. 
A) vertex:
focus: 
B) vertex:
focus: 
C) vertex:
focus: 
D) vertex:
focus: 
E) vertex:
focus: 
A) vertex:
focus: B) vertex:
focus: C) vertex:
focus: D) vertex:
focus: E) vertex:
focus: Question
A solar oven uses a parabolic reflector to focus the sun's rays at a point 6 inches from the vertex of the reflector (see figure). Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin. 
L = 6 inches
A)
B)
C)
D)
E)
L = 6 inchesA)
B)
C)
D)
E)
Question
Sketch the graph of the ellipse, using the latera recta. 
Question
Find the standard form of the equation of the hyperbola with the given characteristics. foci: 
asymptotes: 
A)
B)
C)
D)
E)
asymptotes: A)
B)
C)
D)
E)
Question
Find the vertex and directrix of the parabola. 
A) vertex:
directrix: 
B) vertex:
directrix: 
C) vertex:
directrix: 
D) vertex:
directrix: 
E) vertex:
directrix: 
A) vertex:
directrix: B) vertex:
directrix: C) vertex:
directrix: D) vertex:
directrix: E) vertex:
directrix: Question
Identify the center and radius of the circle. 
A) center: (-3, 4) radius: 4
B) center: (-4, 3) radius: 16
C) center: (-3, 4) radius: 16
D) center: (4, -3) radius: 4
E) center: (3, -4) radius: 16
A) center: (-3, 4) radius: 4
B) center: (-4, 3) radius: 16
C) center: (-3, 4) radius: 16
D) center: (4, -3) radius: 4
E) center: (3, -4) radius: 16
Question
A small submarine is in a narrow underwater canyon 30 feet above the bottom searching for two sunken ships that are known to be 500 feet apart on the canyon floor. The sonar indicates that one of the wrecks is on the bottom in front of the sub, 475 feet from the nose of the sub, and the other wreck is on the bottom directly behind the sub, 75 feet from the nose. The difference in the distance from the wrecks to the sub is constant on a hyperbola having the wrecks as foci. Assume the two wrecks are positioned on a rectangular coordinate system at points with coordinates (-250, 0) and (250, 0) as shown in the figure. Find the x-coordinate of the position of the submarine. (Round to the nearest whole number, if necessary.) 
A) x = 150
B) x = 250
C) x = 38,400
D) x = 200
E) x = 204
A) x = 150
B) x = 250
C) x = 38,400
D) x = 200
E) x = 204
Question
Write the equation of the circle in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the standard form of the equation of the hyperbola with the given characteristics. vertices: 
foci: 
A)
B)
C)
D)
E)
foci: A)
B)
C)
D)
E)
Question
Find the vertices and asymptotes of the hyperbola. 
A) vertices:
asymptote: 
B) vertices:
asymptote: 
C) vertices:
asymptote: 
D) vertices:
asymptote: 
E) vertices:
asymptote: 
A) vertices:
asymptote: B) vertices:
asymptote: C) vertices:
asymptote: D) vertices:
asymptote: E) vertices:
asymptote: Question
Find the standard form of the equation of the ellipse with the following characteristics. foci: 
major axis of length: 12
A)
B)
C)
D)
E)
major axis of length: 12A)
B)
C)
D)
E)
Question
Find the center and vertices of the ellipse. 
A) center: (0, 0) vertices: (0, -7), (0, 7)
B) center: (0, 0) vertices: (-2, 0), (2, 0)
C) center: (7, 2) vertices: (-7, -2), (7, 2)
D) center: (0, 0) vertices: (-7, 0), (7, 0)
E) center: (7, 0) vertices: (0, -2), (0, 2)
A) center: (0, 0) vertices: (0, -7), (0, 7)
B) center: (0, 0) vertices: (-2, 0), (2, 0)
C) center: (7, 2) vertices: (-7, -2), (7, 2)
D) center: (0, 0) vertices: (-7, 0), (7, 0)
E) center: (7, 0) vertices: (0, -2), (0, 2)
Question
Use a graphing utility to graph the parabola. 
Question
Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance) shown in the picture. 
d = 2.75 inches
A)
B)
C)
D)
E)
d = 2.75 inchesA)
B)
C)
D)
E)
Question
Find the center and the vertices of the ellipse. 
A) center: (0, 0) vertices: (-4, 0), (4, 0)
B) center: (0, 0) vertices: (0, -4), (0, 4)
C) center: (-8, 8) vertices: (-2, 0), (2, 0)
D) center: (0, 0) vertices: (-4, -2), (4, 2)
E) center: (-8, 8) vertices: (-2, -4), (2, 4)
A) center: (0, 0) vertices: (-4, 0), (4, 0)
B) center: (0, 0) vertices: (0, -4), (0, 4)
C) center: (-8, 8) vertices: (-2, 0), (2, 0)
D) center: (0, 0) vertices: (-4, -2), (4, 2)
E) center: (-8, 8) vertices: (-2, -4), (2, 4)
Question
Sketch the graph of the ellipse, using the latera recta. 
Question
Sketch the graph of the ellipse, using the latera recta. 
Question
Write the equation of the circle in standard form. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the standard form of the equation of the ellipse with the given characteristics. center: 
foci: 
A)
B)
C)
D)
E)
foci: A)
B)
C)
D)
E)
Question
The path of a rock released from a catapult is modeled by 
. The coordinates x and y are measured in feet, with x = 0 corresponding to the position from which the ball was thrown. Find the highest point and range of the trajectory. Hint: The highest point is the y value of the vertex of the parabola, and the range is the positive x value where y = 0.
A) highest point: 12 ft range: 140 ft
B) highest point: 35 ft range: 140 ft
C) highest point: 12 ft range: 35 ft
D) highest point: 12 ft range:
ft
E) highest point: 35 ft range: 70 ft
. The coordinates x and y are measured in feet, with x = 0 corresponding to the position from which the ball was thrown. Find the highest point and range of the trajectory. Hint: The highest point is the y value of the vertex of the parabola, and the range is the positive x value where y = 0.A) highest point: 12 ft range: 140 ft
B) highest point: 35 ft range: 140 ft
C) highest point: 12 ft range: 35 ft
D) highest point: 12 ft range:
ftE) highest point: 35 ft range: 70 ft
Question
Identify the conic by writing the equation in standard form. 
A)
; hyperbola
B)
; hyperbola
C)
; parabola
D)
; circle
E)
; parabola
A)
; hyperbolaB)
; hyperbolaC)
; parabolaD)
; circleE)
; parabola Question
Find the standard form of the equation of the ellipse with the given characteristics. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Give the standard form of the equation of the parabola with the given characteristics. vertex: (-1, -3) directrix: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the standard form of the equation of the hyperbola with the given characteristics.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Use a graphing utility to graph the parabola. 
Question
Identify the conic by writing the equation in standard form. 
A)
; hyperbola
B)
; hyperbola
C)
; ellipse
D)
; hyperbola
E)
; ellipse
A)
; hyperbolaB)
; hyperbolaC)
; ellipseD)
; hyperbolaE)
; ellipse Question
Identify the conic by writing the equation in standard form. 
A)
; ellipse
B)
; ellipse
C)
; ellipse
D)
; circle
E)
; ellipse
A)
; ellipseB)
; ellipseC)
; ellipseD)
; circleE)
; ellipse Question
Give the standard form of the equation of the parabola with the given characteristics. vertex: (-3, 1) focus: (-1, 1)
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the center and vertices of the hyperbola. 
A) center: (-1, 5), vertices: (-6, 5), (4,5)
B) center: (-1, 5), vertices: (-1, 0), (-1, 10)
C) center: (1,-5), vertices: (-4, -5), (6, -5)
D) center: (1, -5), vertices: (1, -10), (1, 0)
E) center: (-5, 1), vertices: (-10, 1), (0, 1)
A) center: (-1, 5), vertices: (-6, 5), (4,5)
B) center: (-1, 5), vertices: (-1, 0), (-1, 10)
C) center: (1,-5), vertices: (-4, -5), (6, -5)
D) center: (1, -5), vertices: (1, -10), (1, 0)
E) center: (-5, 1), vertices: (-10, 1), (0, 1)
Question
Find the standard form of the equation of the ellipse with the following characteristics.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Give the standard form of the equation of the parabola with the given characteristics. focus: (-1, 0) directrix: 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Identify the conic by writing the equation in standard form. 
A)
; ellipse
B)
; ellipse
C)
; circle
D)
; circle
E)
; circle
A)
; ellipseB)
; ellipseC)
; circleD)
; circleE)
; circle Question
Find the center and foci of the hyperbola. 
A) center: (6, 4), foci: (6, -2), (6, 10)
B) center: (4, 6), foci: (-2, 6), (10, 6)
C) center: (-4, -6), foci: (-4, -12), (-4, 0)
D) center: (-6, -4), foci: (-6, -10), (-6, 2)
E) center: (6, 4), foci: (0, 4), (12, 4)
A) center: (6, 4), foci: (6, -2), (6, 10)
B) center: (4, 6), foci: (-2, 6), (10, 6)
C) center: (-4, -6), foci: (-4, -12), (-4, 0)
D) center: (-6, -4), foci: (-6, -10), (-6, 2)
E) center: (6, 4), foci: (0, 4), (12, 4)
Question
Find the standard form of the equation of the ellipse with the given characteristics. vertices: 
minor axis of length: 6
A)
B)
C)
D)
E)
minor axis of length: 6A)
B)
C)
D)
E)
Question
Find the standard form of the equation of the ellipse with vertices 
and eccentricity 
.
A)
B)
C)
D)
E)
and eccentricity .A)
B)
C)
D)
E)
Question
Find the center and vertices of the ellipse. 
= 0
A) center: (-2, -6) vertices: (-5, -6), (1, -6)
B) center: (-2, -6) vertices: (-3, -6), (-1, -6)
C) center: (6, 2) vertices: (3, 2), (9, 2)
D) center: (2, 6) vertices: (-1, 6), (5, 6)
E) center: (2, 6) vertices: (1, 6), (3, 6)
= 0A) center: (-2, -6) vertices: (-5, -6), (1, -6)
B) center: (-2, -6) vertices: (-3, -6), (-1, -6)
C) center: (6, 2) vertices: (3, 2), (9, 2)
D) center: (2, 6) vertices: (-1, 6), (5, 6)
E) center: (2, 6) vertices: (1, 6), (3, 6)
Question
Find the standard form of the equation of the hyperbola with the given characteristics.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Find the standard form of the equation of the ellipse with vertices 
and eccentricity 
.
A)
B)
C)
D)
E)
and eccentricity .A)
B)
C)
D)
E)
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Deck 5: Rational Functions and Conics
1
Determine the equations of any horizontal and vertical asymptotes of .
A) horizontal: ; vertical:
B) horizontal: ; vertical:
C) horizontal: ; vertical:
D) horizontal: ; vertical:
E) horizontal: ; vertical: none
.A) horizontal:
; vertical: B) horizontal:
; vertical: C) horizontal:
; vertical: D) horizontal:
; vertical: E) horizontal:
; vertical: nonehorizontal: ; vertical:
; vertical: 2
Given :
a. Determine the domains of .
b. Simplify and find any vertical asymptotes.
c. Complete the table.
d. Explain how the two functions differ.
:a. Determine the domains of
.b. Simplify
and find any vertical asymptotes.c. Complete the table.
d. Explain how the two functions differ.
a. Domain of
: all real numbers except -4Domain of
: all real numbersb.
; no vertical asymptotesc.
d. The graph of
except when 
. Because the factor 
canceled, there is a hole in the graph of 
when 
. 3
Given :
a. Determine the domains of .
b. Simplify and find any vertical asymptotes.
c. Complete the table.
d. Explain how the two functions differ.
:a. Determine the domains of
.b. Simplify
and find any vertical asymptotes.c. Complete the table.
d. Explain how the two functions differ.
a. Domain of 
: all real numbers except 
Domain of 
: all real numbers except 0
b.
vertical asymptote 
c.
d. The graph of
except when 
. Because the factor 
canceled, there is a hole in the graph of 
when 
.
: all real numbers except Domain of : all real numbers except 0b.
vertical asymptote c.d. The graph of
except when . Because the factor canceled, there is a hole in the graph of when . 4
Find the domain of .
A) all real numbers except
B) all real numbers except
C) all real numbers except
D) all real numbers except
E) all real numbers
.A) all real numbers except
B) all real numbers except
C) all real numbers except
D) all real numbers except
E) all real numbers
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5
Find the domain of .
A) all real numbers
B) all real numbers except
C) all real numbers except
D) all real numbers except
E) all real numbers except
.A) all real numbers
B) all real numbers except
C) all real numbers except
D) all real numbers except
E) all real numbers except
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6
Determine the equations of any horizontal and vertical asymptotes of .
A) horizontal: none; vertical: none
B) horizontal: ; vertical:
C) horizontal: ; vertical:
D) horizontal: ; vertical:
E) horizontal: ; vertical:
.A) horizontal: none; vertical: none
B) horizontal:
; vertical: C) horizontal:
; vertical: D) horizontal:
; vertical: E) horizontal:
; vertical: Unlock Deck
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7
Determine the zeros (if any) of the rational function .
A)
B) no zeros
C)
D)
E)
.A)
B) no zeros
C)
D)
E)
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8
Determine the zeros (if any) of the rational function .
A)
B) no zeros
C)
D)
E)
.A)
B) no zeros
C)
D)
E)
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9
Determine the equations of the vertical and horizontal asymptotes of the graph of the function .
A) horizontal: ; vertical:
B) horizontal: ; vertical:
C) horizontal: ; vertical:
D) horizontal: ; vertical:
E) horizontal: ; vertical:
.A) horizontal:
; vertical: B) horizontal:
; vertical: C) horizontal:
; vertical: D) horizontal:
; vertical: E) horizontal:
; vertical: Unlock Deck
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10
Determine the equations of any horizontal and vertical asymptotes of .
A) horizontal: ; vertical:
B) horizontal: ; vertical: none
C) horizontal: ; vertical:
D) horizontal: none; vertical: none
E) horizontal: ; vertical: none
.A) horizontal:
; vertical: B) horizontal:
; vertical: noneC) horizontal:
; vertical: D) horizontal: none; vertical: none
E) horizontal:
; vertical: none Unlock Deck
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11
Given :
a. Determine the domains of .
b. Simplify and find any vertical asymptotes.
c. Complete the table. d. Explain how the two functions differ.
:a. Determine the domains of
.b. Simplify
and find any vertical asymptotes.c. Complete the table.
d. Explain how the two functions differ. Unlock Deck
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12
Determine the zeros (if any) of the rational function .
A)
B)
C)
D)
E) no zeros
.A)
B)
C)
D)
E) no zeros
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13
The graph of the function is shown below. Determine the vertical and horizontal asymptotes of its graph.
A) horizontal:
B) horizontal:
C) horizontal:
D) horizontal:
E) horizontal:
is shown below. Determine the vertical and horizontal asymptotes of its graph. A) horizontal:
B) horizontal:
C) horizontal:
D) horizontal:
E) horizontal:
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14
Determine the equations of any horizontal and vertical asymptotes of .
A) horizontal: ; vertical:
B) horizontal: ; vertical:
C) horizontal: ; vertical: none
D) horizontal: ; vertical:
E) horizontal: ; vertical:
.A) horizontal:
; vertical: B) horizontal:
; vertical: C) horizontal:
; vertical: noneD) horizontal:
; vertical: E) horizontal:
; vertical: Unlock Deck
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15
The graph of the function is shown below. Determine the domain.
A)
B)
C)
D)
E)
is shown below. Determine the domain. A)
B)
C)
D)
E)
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16
Determine the domain of .
A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
.A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
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17
Determine the domain of .
A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
.A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
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18
Which of the following is the graph of the given equation?
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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19
Find the domain of .
A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
.A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
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20
Determine the domain of the function .
A) Domain: all real numbers except
B) Domain: all real numbers except
C) Domain: all real numbers except
D) Domain: all real numbers except
E) Domain: all real numbers
.A) Domain: all real numbers except
B) Domain: all real numbers except
C) Domain: all real numbers except
D) Domain: all real numbers except
E) Domain: all real numbers
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21
Given :
a. Determine the domains of .
b. Simplify and find any vertical asymptotes.
c. Complete the table.
d. Explain why a graphing utility may not show the difference in the domains of f and g.
:a. Determine the domains of
.b. Simplify
and find any vertical asymptotes.c. Complete the table.
d. Explain why a graphing utility may not show the difference in the domains of f and g.
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22
A 1500-liter tank contains 30 liters of a 10% acid solution. You add x liters of a 90% acid solution to the tank. Determine a function C that represents the proportion of acid to the total solution in the final mixture.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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23
Determine the equations of any horizontal and vertical asymptotes of .
A) horizontal: none; vertical: none
B) horizontal: ; vertical:
C) horizontal: ; vertical:
D) horizontal: ; vertical:
E) horizontal: ; vertical:
.A) horizontal: none; vertical: none
B) horizontal:
; vertical: C) horizontal:
; vertical: D) horizontal:
; vertical: E) horizontal:
; vertical: Unlock Deck
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24
Find the vertex and focus of the parabola.
A) vertex: (0, 0) focus:
B) vertex: focus:
C) vertex: (0, 0) focus:
D) vertex: focus:
E) vertex: (0, 0) focus:
A) vertex: (0, 0) focus:
B) vertex:
focus: C) vertex: (0, 0) focus:
D) vertex:
focus: E) vertex: (0, 0) focus:
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25
Find the vertex and focus of the parabola.
A) vertex: (0, 0) focus:
B) vertex: focus: (0, 0)
C) vertex: (0, 0) focus:
D) vertex: (0, 0) focus:
E) vertex: focus: (0, 0)
A) vertex: (0, 0) focus:
B) vertex:
focus: (0, 0)C) vertex: (0, 0) focus:
D) vertex: (0, 0) focus:
E) vertex:
focus: (0, 0) Unlock Deck
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26
Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, 7)
A) y2 = 28x
B) x2 = 28y
C) x2 = -7y
D) y2 = 7x
E) x2 = 7y
A) y2 = 28x
B) x2 = 28y
C) x2 = -7y
D) y2 = 7x
E) x2 = 7y
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27
Given , determine the equations of any slant and vertical asymptote.
A) slant: none; vertical: none
B) slant: ; vertical:
C) slant: ; vertical:
D) slant: ; vertical: none
E) slant: ; vertical:
, determine the equations of any slant and vertical asymptote.A) slant: none; vertical: none
B) slant:
; vertical: C) slant:
; vertical: D) slant:
; vertical: noneE) slant:
; vertical: Unlock Deck
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28
Given , determine the equations of any slant and vertical asymptote.
A) slant: ; vertical:
B) slant: ; vertical:
C) slant: ; vertical:
D) slant: ; vertical:
E) slant: ; vertical:
, determine the equations of any slant and vertical asymptote.A) slant:
; vertical: B) slant:
; vertical: C) slant:
; vertical: D) slant:
; vertical: E) slant:
; vertical: Unlock Deck
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29
Solve for any x-intercepts for the graph of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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30
Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 1
A) y2 = -4x
B) y2 = x
C) x2 = 4y
D) x2 = y
E) x2 = -4y
A) y2 = -4x
B) y2 = x
C) x2 = 4y
D) x2 = y
E) x2 = -4y
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31
Solve for any x-intercepts for the graph of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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32
Determine the domain of the function .
A) Domain: all real numbers
B) Domain: all real numbers except
C) Domain: all real numbers except
D) Domain: all real numbers except
E) Domain: all real numbers except
.A) Domain: all real numbers
B) Domain: all real numbers except
C) Domain: all real numbers except
D) Domain: all real numbers except
E) Domain: all real numbers except
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33
Given the rational function :
a. Using a graphing utility, sketch the graph in the given window frame: b. Determine the domain of the function.
c. Identify any vertical asymptotes.
d. Determine the equation of the slant asymptote.
:a. Using a graphing utility, sketch the graph in the given window frame:
b. Determine the domain of the function.c. Identify any vertical asymptotes.
d. Determine the equation of the slant asymptote.
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34
Find the standard form of the equation of the parabola and determine the coordinates of the focus.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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35
Match the equation with its graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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36
A 1500-liter tank contains 70 liters of a 30% acid solution and you add x liters of a 70% acid solution to the tank. If the function C, which represents the proportion of acid to the total solution in the final mixture, is given by , what percent does the concentration of acid appear to be approaching as x increases without bound? (Ignore the physical constraint that .)
A) 100%
B) 30%
C) 40%
D) 70%
E) 20%
, what percent does the concentration of acid appear to be approaching as x increases without bound? (Ignore the physical constraint that .)A) 100%
B) 30%
C) 40%
D) 70%
E) 20%
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37
Solve for any x-intercepts for the graph of .
A)
B)
C)
D)
E)
.A)
B)
C)
D)
E)
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38
Determine the domain of .
A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
.A) all real numbers except
B) all real numbers
C) all real numbers except
D) all real numbers except
E) all real numbers except
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39
A 1500-liter tank contains 70 liters of a 30% acid solution and you add x liters of a 70% acid solution to the tank. If the function C, which represents the proportion of acid to the total solution in the final mixture, is given by , determine the domain based upon the physical constraints of the problem.
A)
B)
C)
D)
E)
, determine the domain based upon the physical constraints of the problem.A)
B)
C)
D)
E)
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40
Given :
a. Determine the domains of .
b. Simplify and find any vertical asymptotes.
c. Complete the table.
d. Explain how the two functions differ.
:a. Determine the domains of
.b. Simplify
and find any vertical asymptotes.c. Complete the table.
d. Explain how the two functions differ.
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41
Find the standard form of the equation of the ellipse with the following graph.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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42
Identify the center and radius of the circle.
A) center: (-6, 0) radius: 7
B) center: (0, -6) radius: 49
C) center: (0, 6) radius: 49
D) center: (0, -6) radius: 7
E) center: (6, 0) radius: 7
A) center: (-6, 0) radius: 7
B) center: (0, -6) radius: 49
C) center: (0, 6) radius: 49
D) center: (0, -6) radius: 7
E) center: (6, 0) radius: 7
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43
Find the vertex and focus of the parabola.
A) vertex: focus:
B) vertex: focus:
C) vertex: focus:
D) vertex: focus:
E) vertex: focus:
A) vertex:
focus: B) vertex:
focus: C) vertex:
focus: D) vertex:
focus: E) vertex:
focus: Unlock Deck
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44
A solar oven uses a parabolic reflector to focus the sun's rays at a point 6 inches from the vertex of the reflector (see figure). Write an equation for a cross section of the oven's reflector with its focus on the positive y axis and its vertex at the origin. L = 6 inches
A)
B)
C)
D)
E)
L = 6 inchesA)
B)
C)
D)
E)
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45
Sketch the graph of the ellipse, using the latera recta.
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46
Find the standard form of the equation of the hyperbola with the given characteristics. foci: asymptotes:
A)
B)
C)
D)
E)
asymptotes: A)
B)
C)
D)
E)
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47
Find the vertex and directrix of the parabola.
A) vertex: directrix:
B) vertex: directrix:
C) vertex: directrix:
D) vertex: directrix:
E) vertex: directrix:
A) vertex:
directrix: B) vertex:
directrix: C) vertex:
directrix: D) vertex:
directrix: E) vertex:
directrix: Unlock Deck
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48
Identify the center and radius of the circle.
A) center: (-3, 4) radius: 4
B) center: (-4, 3) radius: 16
C) center: (-3, 4) radius: 16
D) center: (4, -3) radius: 4
E) center: (3, -4) radius: 16
A) center: (-3, 4) radius: 4
B) center: (-4, 3) radius: 16
C) center: (-3, 4) radius: 16
D) center: (4, -3) radius: 4
E) center: (3, -4) radius: 16
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49
A small submarine is in a narrow underwater canyon 30 feet above the bottom searching for two sunken ships that are known to be 500 feet apart on the canyon floor. The sonar indicates that one of the wrecks is on the bottom in front of the sub, 475 feet from the nose of the sub, and the other wreck is on the bottom directly behind the sub, 75 feet from the nose. The difference in the distance from the wrecks to the sub is constant on a hyperbola having the wrecks as foci. Assume the two wrecks are positioned on a rectangular coordinate system at points with coordinates (-250, 0) and (250, 0) as shown in the figure. Find the x-coordinate of the position of the submarine. (Round to the nearest whole number, if necessary.)
A) x = 150
B) x = 250
C) x = 38,400
D) x = 200
E) x = 204
A) x = 150
B) x = 250
C) x = 38,400
D) x = 200
E) x = 204
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50
Write the equation of the circle in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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51
Find the standard form of the equation of the hyperbola with the given characteristics. vertices: foci:
A)
B)
C)
D)
E)
foci: A)
B)
C)
D)
E)
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52
Find the vertices and asymptotes of the hyperbola.
A) vertices: asymptote:
B) vertices: asymptote:
C) vertices: asymptote:
D) vertices: asymptote:
E) vertices: asymptote:
A) vertices:
asymptote: B) vertices:
asymptote: C) vertices:
asymptote: D) vertices:
asymptote: E) vertices:
asymptote: Unlock Deck
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53
Find the standard form of the equation of the ellipse with the following characteristics. foci: major axis of length: 12
A)
B)
C)
D)
E)
major axis of length: 12A)
B)
C)
D)
E)
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54
Find the center and vertices of the ellipse.
A) center: (0, 0) vertices: (0, -7), (0, 7)
B) center: (0, 0) vertices: (-2, 0), (2, 0)
C) center: (7, 2) vertices: (-7, -2), (7, 2)
D) center: (0, 0) vertices: (-7, 0), (7, 0)
E) center: (7, 0) vertices: (0, -2), (0, 2)
A) center: (0, 0) vertices: (0, -7), (0, 7)
B) center: (0, 0) vertices: (-2, 0), (2, 0)
C) center: (7, 2) vertices: (-7, -2), (7, 2)
D) center: (0, 0) vertices: (-7, 0), (7, 0)
E) center: (7, 0) vertices: (0, -2), (0, 2)
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55
Use a graphing utility to graph the parabola.
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56
Write an equation for a cross section of the parabolic ear (used to hear sounds from a distance) shown in the picture. d = 2.75 inches
A)
B)
C)
D)
E)
d = 2.75 inchesA)
B)
C)
D)
E)
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57
Find the center and the vertices of the ellipse.
A) center: (0, 0) vertices: (-4, 0), (4, 0)
B) center: (0, 0) vertices: (0, -4), (0, 4)
C) center: (-8, 8) vertices: (-2, 0), (2, 0)
D) center: (0, 0) vertices: (-4, -2), (4, 2)
E) center: (-8, 8) vertices: (-2, -4), (2, 4)
A) center: (0, 0) vertices: (-4, 0), (4, 0)
B) center: (0, 0) vertices: (0, -4), (0, 4)
C) center: (-8, 8) vertices: (-2, 0), (2, 0)
D) center: (0, 0) vertices: (-4, -2), (4, 2)
E) center: (-8, 8) vertices: (-2, -4), (2, 4)
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58
Sketch the graph of the ellipse, using the latera recta.
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59
Sketch the graph of the ellipse, using the latera recta.
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60
Write the equation of the circle in standard form.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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61
Find the standard form of the equation of the ellipse with the given characteristics. center: foci:
A)
B)
C)
D)
E)
foci: A)
B)
C)
D)
E)
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62
The path of a rock released from a catapult is modeled by . The coordinates x and y are measured in feet, with x = 0 corresponding to the position from which the ball was thrown. Find the highest point and range of the trajectory. Hint: The highest point is the y value of the vertex of the parabola, and the range is the positive x value where y = 0.
A) highest point: 12 ft range: 140 ft
B) highest point: 35 ft range: 140 ft
C) highest point: 12 ft range: 35 ft
D) highest point: 12 ft range: ft
E) highest point: 35 ft range: 70 ft
. The coordinates x and y are measured in feet, with x = 0 corresponding to the position from which the ball was thrown. Find the highest point and range of the trajectory. Hint: The highest point is the y value of the vertex of the parabola, and the range is the positive x value where y = 0.A) highest point: 12 ft range: 140 ft
B) highest point: 35 ft range: 140 ft
C) highest point: 12 ft range: 35 ft
D) highest point: 12 ft range:
ftE) highest point: 35 ft range: 70 ft
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63
Identify the conic by writing the equation in standard form.
A) ; hyperbola
B) ; hyperbola
C) ; parabola
D) ; circle
E) ; parabola
A)
; hyperbolaB)
; hyperbolaC)
; parabolaD)
; circleE)
; parabola Unlock Deck
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64
Find the standard form of the equation of the ellipse with the given characteristics.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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65
Give the standard form of the equation of the parabola with the given characteristics. vertex: (-1, -3) directrix:
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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66
Find the standard form of the equation of the hyperbola with the given characteristics.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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67
Use a graphing utility to graph the parabola.
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68
Identify the conic by writing the equation in standard form.
A) ; hyperbola
B) ; hyperbola
C) ; ellipse
D) ; hyperbola
E) ; ellipse
A)
; hyperbolaB)
; hyperbolaC)
; ellipseD)
; hyperbolaE)
; ellipse Unlock Deck
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k this deck
69
Identify the conic by writing the equation in standard form.
A) ; ellipse
B) ; ellipse
C) ; ellipse
D) ; circle
E) ; ellipse
A)
; ellipseB)
; ellipseC)
; ellipseD)
; circleE)
; ellipse Unlock Deck
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70
Give the standard form of the equation of the parabola with the given characteristics. vertex: (-3, 1) focus: (-1, 1)
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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71
Find the center and vertices of the hyperbola.
A) center: (-1, 5), vertices: (-6, 5), (4,5)
B) center: (-1, 5), vertices: (-1, 0), (-1, 10)
C) center: (1,-5), vertices: (-4, -5), (6, -5)
D) center: (1, -5), vertices: (1, -10), (1, 0)
E) center: (-5, 1), vertices: (-10, 1), (0, 1)
A) center: (-1, 5), vertices: (-6, 5), (4,5)
B) center: (-1, 5), vertices: (-1, 0), (-1, 10)
C) center: (1,-5), vertices: (-4, -5), (6, -5)
D) center: (1, -5), vertices: (1, -10), (1, 0)
E) center: (-5, 1), vertices: (-10, 1), (0, 1)
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72
Find the standard form of the equation of the ellipse with the following characteristics.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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73
Give the standard form of the equation of the parabola with the given characteristics. focus: (-1, 0) directrix:
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
74
Identify the conic by writing the equation in standard form.
A) ; ellipse
B) ; ellipse
C) ; circle
D) ; circle
E) ; circle
A)
; ellipseB)
; ellipseC)
; circleD)
; circleE)
; circle Unlock Deck
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75
Find the center and foci of the hyperbola.
A) center: (6, 4), foci: (6, -2), (6, 10)
B) center: (4, 6), foci: (-2, 6), (10, 6)
C) center: (-4, -6), foci: (-4, -12), (-4, 0)
D) center: (-6, -4), foci: (-6, -10), (-6, 2)
E) center: (6, 4), foci: (0, 4), (12, 4)
A) center: (6, 4), foci: (6, -2), (6, 10)
B) center: (4, 6), foci: (-2, 6), (10, 6)
C) center: (-4, -6), foci: (-4, -12), (-4, 0)
D) center: (-6, -4), foci: (-6, -10), (-6, 2)
E) center: (6, 4), foci: (0, 4), (12, 4)
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76
Find the standard form of the equation of the ellipse with the given characteristics. vertices: minor axis of length: 6
A)
B)
C)
D)
E)
minor axis of length: 6A)
B)
C)
D)
E)
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77
Find the standard form of the equation of the ellipse with vertices and eccentricity .
A)
B)
C)
D)
E)
and eccentricity .A)
B)
C)
D)
E)
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78
Find the center and vertices of the ellipse. = 0
A) center: (-2, -6) vertices: (-5, -6), (1, -6)
B) center: (-2, -6) vertices: (-3, -6), (-1, -6)
C) center: (6, 2) vertices: (3, 2), (9, 2)
D) center: (2, 6) vertices: (-1, 6), (5, 6)
E) center: (2, 6) vertices: (1, 6), (3, 6)
= 0A) center: (-2, -6) vertices: (-5, -6), (1, -6)
B) center: (-2, -6) vertices: (-3, -6), (-1, -6)
C) center: (6, 2) vertices: (3, 2), (9, 2)
D) center: (2, 6) vertices: (-1, 6), (5, 6)
E) center: (2, 6) vertices: (1, 6), (3, 6)
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79
Find the standard form of the equation of the hyperbola with the given characteristics.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
80
Find the standard form of the equation of the ellipse with vertices and eccentricity .
A)
B)
C)
D)
E)
and eccentricity .A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 80 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 80 flashcards in this deck.
