Question 1

Determine the domain of the function   .

Accepted Answer

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 2

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.

Accepted Answer

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 
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

Question 3

Solve for any x-intercepts for the graph of   .

Accepted Answer

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

Question 4

Determine the equations of any horizontal and vertical asymptotes of   .

Accepted Answer

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 5

Find the vertex and directrix of the parabola.

Accepted Answer

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 6

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

Accepted Answer

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

Question 7

Find the vertex and focus of the parabola.

Accepted Answer

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 8

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

Accepted Answer

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

Question 9

Solve for any x-intercepts for the graph of   .

Accepted Answer

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

Question 10

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

Accepted Answer

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

Question 11

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 12

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

Accepted Answer

A)  slant: none; vertical: none 
B)  slant:   ; vertical:   
C)  slant:   ; vertical:   
D)  slant:   ; vertical: none 
E)  slant:   ; vertical:   
A)  slant: none; vertical: none 
B)  slant:   ; vertical:   
C)  slant:   ; vertical:   
D)  slant:   ; vertical: none 
E)  slant:   ; vertical:

Question 13

Find the standard form of the equation of the ellipse with the given characteristics. vertices:   minor axis of length: 6

Accepted Answer

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

Question 14

Give the standard form of the equation of the parabola with the given characteristics. focus: (-1, 0) directrix:

Accepted Answer

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

Question 15

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.

Accepted Answer

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

Question 16

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.

Accepted Answer

a. @#IMG-DLM& 
b. al

Question 17

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.

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Determine the domain of the function   .

Accepted Answer

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 20

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:

Determine the domain of the function .

Solve for any x-intercepts for the graph of .

Determine the equations of any horizontal and vertical asymptotes of .

Find the vertex and directrix of the parabola.

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

Find the vertex and focus of the parabola.

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

Solve for any x-intercepts for the graph of .

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

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

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

Find the standard form of the equation of the ellipse with the given characteristics. vertices: minor axis of length: 6

Give the standard form of the equation of the parabola with the given characteristics. focus: (-1, 0) directrix:

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.

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.

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

Determine the domain of the function .

Determine the equations of any horizontal and vertical asymptotes of .

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

Determine the domain of the function .

Solve for any x-intercepts for the graph of .

Determine the equations of any horizontal and vertical asymptotes of .

Find the vertex and directrix of the parabola.

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

Find the vertex and focus of the parabola.

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

Solve for any x-intercepts for the graph of .

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

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

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

Find the standard form of the equation of the ellipse with the given characteristics. vertices: minor axis of length: 6

Give the standard form of the equation of the parabola with the given characteristics. focus: (-1, 0) directrix:

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.

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.

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

Determine the domain of the function .

Determine the equations of any horizontal and vertical asymptotes of .

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