Question 1

Identify the conic by writing the equation in standard form.

Accepted Answer

A)    ; ellipse 
B)    ; ellipse 
C)    ; circle 
D)    ; circle 
E)    ; circle 
A)    ; ellipse 
B)    ; ellipse 
C)    ; circle 
D)    ; circle 
E)    ; circle

Question 2

Find the domain of   .

Accepted Answer

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 3

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-3, 1) focus: (-1, 1)

Accepted Answer

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

Question 4

Find the center and foci of the hyperbola.

Accepted Answer

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 5

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 6

Write the equation of the circle in standard form.

Accepted Answer

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

Question 7

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

Accepted Answer

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

Question 8

Identify the conic by writing the equation in standard form.

Accepted Answer

A)    ; ellipse 
B)    ; ellipse 
C)    ; ellipse 
D)    ; circle 
E)    ; ellipse 
A)    ; ellipse 
B)    ; ellipse 
C)    ; ellipse 
D)    ; circle 
E)    ; ellipse

Question 9

Sketch the graph of the ellipse, using the latera recta.

Accepted Answer

The answer of Sketch the graph of the ellipse, using...

Question 10

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 1

Accepted Answer

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

Question 11

Identify the conic by writing the equation in standard form.

Accepted Answer

A)    ; hyperbola 
B)    ; hyperbola 
C)    ; ellipse 
D)    ; hyperbola 
E)    ; ellipse 
A)    ; hyperbola 
B)    ; hyperbola 
C)    ; ellipse 
D)    ; hyperbola 
E)    ; ellipse

Question 12

Find the standard form of the equation of the ellipse with the given characteristics. center:     foci:

Accepted Answer

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

Question 13

Match the equation with its graph.

Accepted Answer

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

Question 14

Find the vertices and asymptotes of the hyperbola.

Accepted Answer

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 15

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 16

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 17

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-1, -3) directrix:

Accepted Answer

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

Question 18

Find 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 19

Which of the following is the graph of the given equation?

Accepted Answer

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

Question 20

Identify the center and radius of the circle.

Accepted Answer

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

Identify the conic by writing the equation in standard form.

Find the domain of .

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-3, 1) focus: (-1, 1)

Find the center and foci of the hyperbola.

Determine the domain of .

Write the equation of the circle in standard form.

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

Identify the conic by writing the equation in standard form.

Sketch the graph of the ellipse, using the latera recta.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 1

Identify the conic by writing the equation in standard form.

Find the standard form of the equation of the ellipse with the given characteristics. center: foci:

Match the equation with its graph.

Find the vertices and asymptotes of the hyperbola.

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

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

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-1, -3) directrix:

Find the domain of .

Which of the following is the graph of the given equation?

Identify the center and radius of the circle.

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

Identify the conic by writing the equation in standard form.

Find the domain of .

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-3, 1) focus: (-1, 1)

Find the center and foci of the hyperbola.

Determine the domain of .

Write the equation of the circle in standard form.

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

Identify the conic by writing the equation in standard form.

Sketch the graph of the ellipse, using the latera recta.

Find the standard form of the equation of the parabola with the given characteristic and vertex at the origin. directrix: x = 1

Identify the conic by writing the equation in standard form.

Find the standard form of the equation of the ellipse with the given characteristics. center: foci:

Match the equation with its graph.

Find the vertices and asymptotes of the hyperbola.

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

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

Give the standard form of the equation of the parabola with the given characteristics. vertex: (-1, -3) directrix:

Find the domain of .

Which of the following is the graph of the given equation?

Identify the center and radius of the circle.

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