Question 1

Use a graphing utility to graph the parabola.

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 2

The graph of the function   is shown below. Determine the vertical and horizontal asymptotes of its graph.

Accepted Answer

A)  horizontal:     
B)  horizontal:     
C)  horizontal:     
D)  horizontal:     
E)  horizontal:     
A)  horizontal:     
B)  horizontal:     
C)  horizontal:     
D)  horizontal:     
E)  horizontal:     C

Question 3

Determine the equations of any horizontal and vertical asymptotes of   .

Accepted Answer

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: none 
D)  horizontal:   ; vertical:   
E)  horizontal:   ; vertical:   C

Question 4

Find the center and vertices of the hyperbola.

Accepted Answer

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 5

Find the center and vertices of the ellipse.

Accepted Answer

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 6

Use a graphing utility to graph the parabola.

Accepted Answer

The answer of Use a graphing utility to graph the...

Question 7

Find the standard form of the equation of the ellipse with vertices   and eccentricity   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 8

Find the center and vertices of the ellipse.   = 0

Accepted Answer

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) 
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)

Question 9

Find the standard form of the equation of the hyperbola with the given characteristics. foci:   asymptotes:

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

Given   :
a. Determine the domains of   .
b. Simplify   and find any vertical asymptotes.
c. Complete the table.
d. Explain how the two functions differ.

Accepted Answer

a. Domain of @#IMG-DLM& : all real numbers except

Question 11

Find the standard form of the equation of the ellipse with the following characteristics.

Accepted Answer

A)      
B)    
C)    
D)    
E)    
A)      
B)    
C)    
D)    
E)

Question 12

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.)

Accepted Answer

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 13

Identify the center and radius of the circle.

Accepted Answer

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 14

Write the equation of the circle in standard form.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 15

Find the domain of   .

Accepted Answer

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 16

Determine the zeros (if any) of the rational function   .

Accepted Answer

A)    
B)  no zeros 
C)    
D)    
E)    
A)    
B)  no zeros 
C)    
D)    
E)

Question 17

Find the standard form of the equation of the ellipse with the following characteristics. foci:   major axis of length: 12

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 18

Find the standard form of the equation of the ellipse with the following graph.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Determine the domain of   .

Accepted Answer

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 20

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, 7)

Accepted Answer

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

Use a graphing utility to graph the parabola.

The graph of the function is shown below. Determine the vertical and horizontal asymptotes of its graph.

Determine the equations of any horizontal and vertical asymptotes of .

Find the center and vertices of the hyperbola.

Find the center and vertices of the ellipse.

Use a graphing utility to graph the parabola.

Find the standard form of the equation of the ellipse with vertices and eccentricity .

Find the center and vertices of the ellipse. = 0

Find the standard form of the equation of the hyperbola with the given characteristics. foci: asymptotes:

Given : a. Determine the domains of . b. Simplify and find any vertical asymptotes. c. Complete the table. d. Explain how the two functions differ.

Find the standard form of the equation of the ellipse with the following characteristics.

Identify the center and radius of the circle.

Write the equation of the circle in standard form.

Find the domain of .

Determine the zeros (if any) of the rational function .

Find the standard form of the equation of the ellipse with the following characteristics. foci: major axis of length: 12

Find the standard form of the equation of the ellipse with the following graph.

Determine the domain of .

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, 7)

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Polynomial Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Filters

Exam 5: Rational Functions and Conics

Use a graphing utility to graph the parabola.

The graph of the function is shown below. Determine the vertical and horizontal asymptotes of its graph.

Determine the equations of any horizontal and vertical asymptotes of .

Find the center and vertices of the hyperbola.

Find the center and vertices of the ellipse.

Use a graphing utility to graph the parabola.

Find the standard form of the equation of the ellipse with vertices and eccentricity .

Find the center and vertices of the ellipse. = 0

Find the standard form of the equation of the hyperbola with the given characteristics. foci: asymptotes:

Given : a. Determine the domains of . b. Simplify and find any vertical asymptotes. c. Complete the table. d. Explain how the two functions differ.

Find the standard form of the equation of the ellipse with the following characteristics.

Identify the center and radius of the circle.

Write the equation of the circle in standard form.

Find the domain of .

Determine the zeros (if any) of the rational function .

Find the standard form of the equation of the ellipse with the following characteristics. foci: major axis of length: 12

Find the standard form of the equation of the ellipse with the following graph.

Determine the domain of .

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. focus: (0, 7)

Prerequisites

Equations, Inequalities, and Mathematical Modeling

Functions and Their Graphs

Polynomial Functions

Exponential and Logarithmic Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Filters