Question 1

Find the domain of the function. ​​ $$g ( s ) = \frac { - 3 s } { s - 9 }$$ ​

Accepted Answer

A) s = 9 
B) all real numbers s ≠ 9,s ≠ 0 
C) ​s = 9,s = 0 
D) all real numbers s ≠ 9 
E)  $$\varnothing$$ 
A) s = 9 
B) all real numbers s ≠ 9,s ≠ 0 
C) ​s = 9,s = 0 
D) all real numbers s ≠ 9 
E)  $$\varnothing$$

Question 2

Find domain of the following function.​ $$g ( x ) = \frac { 1 - 9 x } { 1 - x }$$ ​

Accepted Answer

A) all real numbers x 
B) all real numbers x except x = 1 
C) all real numbers x except x = -9 
D) all real numbers x except x = -1 
E) all real numbers x except x = 9 
A) all real numbers x 
B) all real numbers x except x = 1 
C) all real numbers x except x = -9 
D) all real numbers x except x = -1 
E) all real numbers x except x = 9

Question 3

Find the domain of the function and identify any vertical and horizontal asymptotes.​ $$f ( x ) = \frac { x + 4 } { x ^ { 2 } - 16 }$$ ​

Accepted Answer

A) The domain is all real numbers x except x = ±4.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0. 
B) The domain is all real numbers x except x = ±4.There is a vertical asymptote at x = -16,and a horizontal asymptote at y = 0. 
C) The domain is all real numbers x except x = ±16.There is a vertical asymptote at x = -16,and a horizontal asymptote at y = 0. 
D) The domain is all real numbers x except x = ±4.There is a vertical asymptote at x = 4,and a horizontal asymptote at y = 0. 
E) The domain is all real numbers x except x = ±16.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0. 
A) The domain is all real numbers x except x = ±4.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0. 
B) The domain is all real numbers x except x = ±4.There is a vertical asymptote at x = -16,and a horizontal asymptote at y = 0. 
C) The domain is all real numbers x except x = ±16.There is a vertical asymptote at x = -16,and a horizontal asymptote at y = 0. 
D) The domain is all real numbers x except x = ±4.There is a vertical asymptote at x = 4,and a horizontal asymptote at y = 0. 
E) The domain is all real numbers x except x = ±16.There is a vertical asymptote at x = -4,and a horizontal asymptote at y = 0.

Question 4

Given $f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }$ ,determine the equations of any slant and vertical asymptote.

Accepted Answer

A) slant: y = x - 3;vertical: x = 3 
B) slant: y = x + 3;vertical: x = 7 
C) slant: none;vertical: none 
D) slant: y = x - 11;vertical: none 
E) slant: y = x + 10;vertical: x = -4 
A) slant: y = x - 3;vertical: x = 3 
B) slant: y = x + 3;vertical: x = 7 
C) slant: none;vertical: none 
D) slant: y = x - 11;vertical: none 
E) slant: y = x + 10;vertical: x = -4

Question 5

Find domain of the following function. $$g ( x ) = \frac { x ^ { 2 } - 49 } { x ^ { 2 } - 6 x - 7 }$$ ​

Accepted Answer

A) all real numbers x except x = -49 and x = -1 
B) all real numbers x except x = -6 and x = ​7 
C) all real numbers x except x = 6 and x = 49 
D) all real numbers x except x = 7 and x = -1 
E) all real numbers x except x = -7 and x = 1 
A) all real numbers x except x = -49 and x = -1 
B) all real numbers x except x = -6 and x = ​7 
C) all real numbers x except x = 6 and x = 49 
D) all real numbers x except x = 7 and x = -1 
E) all real numbers x except x = -7 and x = 1

Question 6

Determine the value that the function f approaches as the magnitude of x increases.​ $f ( x ) = 2 - \frac { 4 } { x }$ ​

Accepted Answer

A) 1 
B) -4 
C) 2 
D) -2 
E) -1.75 
A) 1 
B) -4 
C) 2 
D) -2 
E) -1.75

Question 7

The graph of the function ​​ $$f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 }$$ is shown below.Determine the domain.

Accepted Answer

A) Domain: all real numbers except x = -2 and x = 2 
B) Domain: all real numbers except x = 2 
C) Domain: all real numbers except x = 0 
D) Domain: all real numbers except x = 4 
A) Domain: all real numbers except x = -2 and x = 2 
B) Domain: all real numbers except x = 2 
C) Domain: all real numbers except x = 0 
D) Domain: all real numbers except x = 4

Question 8

Determine the equations of any horizontal and vertical asymptotes of $$f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 4 }$$ .

Accepted Answer

A) horizontal: y = 2;vertical: x = -2 
B) horizontal: x = 1;vertical: none 
C) horizontal: none;vertical: none 
D) horizontal: y = 1;vertical: none 
E) horizontal: y = -2;vertical: x = 1 
A) horizontal: y = 2;vertical: x = -2 
B) horizontal: x = 1;vertical: none 
C) horizontal: none;vertical: none 
D) horizontal: y = 1;vertical: none 
E) horizontal: y = -2;vertical: x = 1

Question 9

Find the domain of $$f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }$$ .

Accepted Answer

A) all real numbers except x = 8 and x = -4 
B) all real numbers 
C) all real numbers except x = 4 and x = -8 
D) all real numbers except x = -4,x = 4 and x = -8 
E) all real numbers except x = -8 
A) all real numbers except x = 8 and x = -4 
B) all real numbers 
C) all real numbers except x = 4 and x = -8 
D) all real numbers except x = -4,x = 4 and x = -8 
E) all real numbers except x = -8

Question 10

Select the correct graph of the function $$f ( x ) = \frac { 6 } { x + 4 }$$ . ​

Accepted Answer

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

Question 11

The cost C (in millions of dollars)of removing p% of the industrial and municipal pollutants discharged into a river is given by​ $C = \frac { 235 p } { 100 - p } , 0 \leq p \leq 100$ .
​
Find the costs of removing 70% of the pollutants.
(Round your answer to two decimal places. )
​

Accepted Answer

A) $568.33 million 
B) $588.33 million 
C) $578.33 million 
D) $558.33 million 
E) $548.33 million 
A) $568.33 million 
B) $588.33 million 
C) $578.33 million 
D) $558.33 million 
E) $548.33 million

Question 12

Determine the zeros (if any)of the rational function $g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }$ .

Accepted Answer

A)  $x = - \sqrt { 5 } , x = \sqrt { 5 }$ 
B) x = -4 
C)  $x = - \frac { 4 } { 5 } , x = \frac { 4 } { 5 }$ 
D) x = -5,x = 5 
E) no zeros 
A)  $x = - \sqrt { 5 } , x = \sqrt { 5 }$ 
B) x = -4 
C)  $x = - \frac { 4 } { 5 } , x = \frac { 4 } { 5 }$ 
D) x = -5,x = 5 
E) no zeros

Question 13

Find the domain of $f ( x ) = \frac { x - 7 } { x ^ { 2 } - 49 }$ .

Accepted Answer

A) all real numbers except x = -7 
B) all real numbers except x = 49 
C) all real numbers except x = 7 
D) all real numbers except x = 7 and x = -7 
E) all real numbers 
A) all real numbers except x = -7 
B) all real numbers except x = 49 
C) all real numbers except x = 7 
D) all real numbers except x = 7 and x = -7 
E) all real numbers

Question 14

Select the correct graph of the following function.​ $$f ( x ) = \frac { x ^ { 2 } + 6 } { x }$$ ​

Accepted Answer

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

Question 15

Find the domain of the function and identify any vertical and horizontal asymptotes.​ $$f ( x ) = \frac { 5 x ^ { 2 } + 8 } { x ^ { 2 } + x + 9 }$$ ​

Accepted Answer

A) Domain: all real numbers x Vertical asymptote: No vertical asymptote
Horizontal asymptote: y = 5 
B) Domain: all real numbers except x = 0 Vertical asymptote: x = 0
Horizontal asymptote: y = -8 
C) Domain: all real numbers x Vertical asymptote: x = -5
Horizontal asymptote: y = 0 
D) Domain: all real numbers except x = 5 Vertical asymptote: No vertical asymptote
Horizontal asymptote: No horizontal asymptote 
E) Domain: all real numbers except x = 9 Vertical asymptote: x = 5
Horizontal asymptote: y = 8 
A) Domain: all real numbers x Vertical asymptote: No vertical asymptote
Horizontal asymptote: y = 5 
B) Domain: all real numbers except x = 0 Vertical asymptote: x = 0
Horizontal asymptote: y = -8 
C) Domain: all real numbers x Vertical asymptote: x = -5
Horizontal asymptote: y = 0 
D) Domain: all real numbers except x = 5 Vertical asymptote: No vertical asymptote
Horizontal asymptote: No horizontal asymptote 
E) Domain: all real numbers except x = 9 Vertical asymptote: x = 5
Horizontal asymptote: y = 8

Question 16

Determine the equations of any horizontal and vertical asymptotes of $$f ( x ) = \frac { 2 x ^ { 2 } - x - 9 } { x ^ { 2 } + 3 x + 3 }$$ .

Accepted Answer

A) horizontal: y = 4;vertical: x = 0 
B) horizontal: y = - 3;vertical: x = -4 
C) horizontal: y = 2;vertical: none 
D) horizontal: y = 1;vertical: x = - 3 
E) horizontal: y = -2;vertical: x = 3 and x = -4 
A) horizontal: y = 4;vertical: x = 0 
B) horizontal: y = - 3;vertical: x = -4 
C) horizontal: y = 2;vertical: none 
D) horizontal: y = 1;vertical: x = - 3 
E) horizontal: y = -2;vertical: x = 3 and x = -4

Question 17

Find the domain of the function and identify any vertical and horizontal asymptotes.​ $$f ( x ) = \frac { 7 + x } { 7 - x }$$ ​

Accepted Answer

A) Domain: all real numbers x except x = 7 Vertical asymptote: x = 7
Horizontal asymptote: y = -1 
B) Domain: all real numbers x Vertical asymptote: x = -7
Horizontal asymptote: y = 0 
C) Domain: all real numbers x except x = 0 Vertical asymptote: x = 0
Horizontal asymptote: y = -1 
D) Domain: all real numbers x except x = 7 Vertical asymptote: x = 0
Horizontal asymptote: y = -7 
E) Domain: all real numbers x except x = -7 Vertical asymptote: x = 0
Horizontal asymptote: y = 7 
A) Domain: all real numbers x except x = 7 Vertical asymptote: x = 7
Horizontal asymptote: y = -1 
B) Domain: all real numbers x Vertical asymptote: x = -7
Horizontal asymptote: y = 0 
C) Domain: all real numbers x except x = 0 Vertical asymptote: x = 0
Horizontal asymptote: y = -1 
D) Domain: all real numbers x except x = 7 Vertical asymptote: x = 0
Horizontal asymptote: y = -7 
E) Domain: all real numbers x except x = -7 Vertical asymptote: x = 0
Horizontal asymptote: y = 7

Question 18

The game commission introduces 100 deer into newly acquired state game lands.The population N of the herd is modeled by​ $N = \frac { 24 ( 5 + 3 t ) } { 1 + 0.04 t } , t \geq 0$ ​ where t is the time in years.Find the populations when t = 40.
(Round your answer to the nearest whole number. )
​

Accepted Answer

A) 1,154 deer 
B) 1,306 deer 
C) 1,275 deer 
D) 1,240 deer 
E) 1,200 deer 
A) 1,154 deer 
B) 1,306 deer 
C) 1,275 deer 
D) 1,240 deer 
E) 1,200 deer

Question 19

Find the zeros of the rational function.​ $$f ( x ) = 1 - \frac { 5 } { x - 10 }$$ ​

Accepted Answer

A) x = -15 
B) x = -5 
C) x = 15 
D) x = -10 
E) x = 5 
A) x = -15 
B) x = -5 
C) x = 15 
D) x = -10 
E) x = 5

Question 20

Which of the following is the graph of the given equation?​ $$f ( x ) = \frac { 2 - x } { x + 3 }$$ ​

Accepted Answer

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

Exam 16: Rational Functions

Find the domain of the function. ​​ g(s)=−3ss−9g ( s ) = \frac { - 3 s } { s - 9 }g(s)=s−9−3s​ ​

Find domain of the following function.​ g(x)=1−9x1−xg ( x ) = \frac { 1 - 9 x } { 1 - x }g(x)=1−x1−9x​ ​

Find the domain of the function and identify any vertical and horizontal asymptotes.​ f(x)=x+4x2−16f ( x ) = \frac { x + 4 } { x ^ { 2 } - 16 }f(x)=x2−16x+4​ ​

Given f(x)=x2−4x+3x−7f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }f(x)=x−7x2−4x+3​ ,determine the equations of any slant and vertical asymptote.

Find domain of the following function. g(x)=x2−49x2−6x−7g ( x ) = \frac { x ^ { 2 } - 49 } { x ^ { 2 } - 6 x - 7 }g(x)=x2−6x−7x2−49​ ​

Determine the value that the function f approaches as the magnitude of x increases.​ f(x)=2−4xf ( x ) = 2 - \frac { 4 } { x }f(x)=2−x4​ ​

The graph of the function ​​ f(x)=3xx2−4f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 }f(x)=x2−43x​ is shown below.Determine the domain.

Determine the equations of any horizontal and vertical asymptotes of f(x)=x2x2+4f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 4 }f(x)=x2+4x2​ .

Find the domain of f(x)=x2−16x2+4x−32f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }f(x)=x2+4x−32x2−16​ .

Select the correct graph of the function f(x)=6x+4f ( x ) = \frac { 6 } { x + 4 }f(x)=x+46​ . ​

Determine the zeros (if any)of the rational function g(x)=5+4x2+5g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }g(x)=5+x2+54​ .

Find the domain of f(x)=x−7x2−49f ( x ) = \frac { x - 7 } { x ^ { 2 } - 49 }f(x)=x2−49x−7​ .

Select the correct graph of the following function.​ f(x)=x2+6xf ( x ) = \frac { x ^ { 2 } + 6 } { x }f(x)=xx2+6​ ​

Find the domain of the function and identify any vertical and horizontal asymptotes.​ f(x)=5x2+8x2+x+9f ( x ) = \frac { 5 x ^ { 2 } + 8 } { x ^ { 2 } + x + 9 }f(x)=x2+x+95x2+8​ ​

Determine the equations of any horizontal and vertical asymptotes of f(x)=2x2−x−9x2+3x+3f ( x ) = \frac { 2 x ^ { 2 } - x - 9 } { x ^ { 2 } + 3 x + 3 }f(x)=x2+3x+32x2−x−9​ .

Find the domain of the function and identify any vertical and horizontal asymptotes.​ f(x)=7+x7−xf ( x ) = \frac { 7 + x } { 7 - x }f(x)=7−x7+x​ ​

Find the zeros of the rational function.​ f(x)=1−5x−10f ( x ) = 1 - \frac { 5 } { x - 10 }f(x)=1−x−105​ ​

Which of the following is the graph of the given equation?​ f(x)=2−xx+3f ( x ) = \frac { 2 - x } { x + 3 }f(x)=x+32−x​ ​

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

Hyperbolas

Find the domain of the function. $g ( s ) = \frac { - 3 s } { s - 9 }$

Find domain of the following function. $g ( x ) = \frac { 1 - 9 x } { 1 - x }$

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { x + 4 } { x ^ { 2 } - 16 }$

Given $f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x - 7 }$ ,determine the equations of any slant and vertical asymptote.

Find domain of the following function. $g ( x ) = \frac { x ^ { 2 } - 49 } { x ^ { 2 } - 6 x - 7 }$

Determine the value that the function f approaches as the magnitude of x increases. $f ( x ) = 2 - \frac { 4 } { x }$

The graph of the function $f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 }$ is shown below.Determine the domain. $The graph of the function f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 } is shown below.Determine the domain.$

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 4 }$ .

Find the domain of $f ( x ) = \frac { x ^ { 2 } - 16 } { x ^ { 2 } + 4 x - 32 }$ .

Select the correct graph of the function $f ( x ) = \frac { 6 } { x + 4 }$ .

Determine the zeros (if any)of the rational function $g ( x ) = 5 + \frac { 4 } { x ^ { 2 } + 5 }$ .

Find the domain of $f ( x ) = \frac { x - 7 } { x ^ { 2 } - 49 }$ .

Select the correct graph of the following function. $f ( x ) = \frac { x ^ { 2 } + 6 } { x }$

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { 5 x ^ { 2 } + 8 } { x ^ { 2 } + x + 9 }$

Determine the equations of any horizontal and vertical asymptotes of $f ( x ) = \frac { 2 x ^ { 2 } - x - 9 } { x ^ { 2 } + 3 x + 3 }$ .

Find the domain of the function and identify any vertical and horizontal asymptotes. $f ( x ) = \frac { 7 + x } { 7 - x }$

Find the zeros of the rational function. $f ( x ) = 1 - \frac { 5 } { x - 10 }$

Which of the following is the graph of the given equation? $f ( x ) = \frac { 2 - x } { x + 3 }$