Question 1

Find the center and the vertices of the ellipse.

Accepted Answer

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 2

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Accepted Answer

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

Question 3

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 4

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

Accepted Answer

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

Question 5

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 6

Determine the equations of any horizontal and vertical asymptotes of   .

Accepted Answer

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 7

Given   , determine the equations of any slant and vertical asymptote.

Accepted Answer

A)  slant:   ; vertical:   
B)  slant:   ; vertical:   
C)  slant:   ; vertical:   
D)  slant:   ; vertical:   
E)  slant:   ; vertical:   
A)  slant:   ; vertical:   
B)  slant:   ; vertical:   
C)  slant:   ; vertical:   
D)  slant:   ; vertical:   
E)  slant:   ; vertical:

Question 8

Find the vertex and focus of the parabola.

Accepted Answer

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 9

Determine the equations of any horizontal and vertical asymptotes of   .

Accepted Answer

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

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

Solve for any x-intercepts for the graph of   .

Accepted Answer

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

Question 12

Determine the equations of the vertical and horizontal asymptotes of the graph of the function   .

Accepted Answer

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 13

Identify the conic by writing the equation in standard form.

Accepted Answer

A)    ; hyperbola 
B)    ; hyperbola 
C)    ; parabola 
D)    ; circle 
E)    ; parabola 
A)    ; hyperbola 
B)    ; hyperbola 
C)    ; parabola 
D)    ; circle 
E)    ; parabola

Question 14

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 15

The graph of the function   is shown below. Determine the domain.

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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   .)

Accepted Answer

A)  100% 
B)  30% 
C)  40% 
D)  70% 
E)  20% 
A)  100% 
B)  30% 
C)  40% 
D)  70% 
E)  20%

Question 19

Find the vertex and focus of the parabola.

Accepted Answer

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 20

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.

Accepted Answer

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

Find the center and the vertices of the ellipse.

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Determine the domain of .

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

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

Determine the equations of any horizontal and vertical asymptotes of .

Given , determine the equations of any slant and vertical asymptote.

Find the vertex and focus of the parabola.

Determine the equations of any horizontal and vertical asymptotes of .

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

Solve for any x-intercepts for the graph of .

Determine the equations of the vertical and horizontal asymptotes of the graph of the function .

Identify the conic by writing the equation in standard form.

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

The graph of the function is shown below. Determine the domain.

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

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

Find the vertex and focus of the parabola.

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.

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

Find the center and the vertices of the ellipse.

Find the standard form of the equation of the parabola and determine the coordinates of the focus.

Determine the domain of .

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

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

Determine the equations of any horizontal and vertical asymptotes of .

Given , determine the equations of any slant and vertical asymptote.

Find the vertex and focus of the parabola.

Determine the equations of any horizontal and vertical asymptotes of .

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

Solve for any x-intercepts for the graph of .

Determine the equations of the vertical and horizontal asymptotes of the graph of the function .

Identify the conic by writing the equation in standard form.

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

The graph of the function is shown below. Determine the domain.

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

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

Find the vertex and focus of the parabola.

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.

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