Question 1

Find the asymptote(s) of the given function.
-$f ( x ) = \frac { x - 3 } { x ^ { 2 } - 36 }$ vertical asymptotes(s)

Accepted Answer

A)  $x = - 6$ 
B)  $x = 3$ 
C)  $x = 6 , x = - 6$ 
D)  $x = 6$ 
A)  $x = - 6$ 
B)  $x = 3$ 
C)  $x = 6 , x = - 6$ 
D)  $x = 6$ C

Question 2

Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is
removable or non-removable.
-$$g ( x ) = \frac { x ^ { 2 } - 3 x } { x }$$

Accepted Answer

A)

No 
B) 
 
No 
C) 
 
Yes; removable 
D)

No 
A)

No 
B) 
 
No 
C) 
 
Yes; removable 
D)

No C

Question 3

Solve the problem.
-A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a $4 - \mathrm { km }$ by 6-km rectangle. As the camera zooms out, the length 1 and width $w$ of the rectangle increase at a rate of 3 $\mathrm { km } / \mathrm { sec }$. How long does it take for the area A to be at least 4 times its original size?

Accepted Answer

A)  $1.61 \mathrm { sec }$ 
B)  $9.7 \mathrm { sec }$ 
C)  $4.94 \mathrm { sec }$ 
D)  $3.28 \mathrm { sec }$ 
A)  $1.61 \mathrm { sec }$ 
B)  $9.7 \mathrm { sec }$ 
C)  $4.94 \mathrm { sec }$ 
D)  $3.28 \mathrm { sec }$ A

Question 4

Perform the requested operation or operations. Find the domain of each.
-$$f ( x ) = \sqrt { x } ; g ( x ) = 6 x - 7$$
Find $f / g$.

Accepted Answer

A)  $( \mathrm { f } / \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 6 \mathrm { x } - 7 } ;$ domain $\left\{ x \mid x \geq 0 , x \neq \frac { 7 } { 6 } \right\}$ 
B)  $( f / g ) ( x ) = \frac { 6 x - 7 } { \sqrt { x } } ;$ domain $\{ x \mid x \geq 0 \}$ 
C)  $( \mathrm { f } / \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 6 \mathrm { x } - 7 }$; domain $\{ x \mid x \neq 0 \}$ 
D)  $( \mathrm { f } / \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 6 \mathrm { x } - 7 } ;$ domain $\left\{ x \mid x \neq \frac { 7 } { 6 } \right\}$ 
A)  $( \mathrm { f } / \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 6 \mathrm { x } - 7 } ;$ domain $\left\{ x \mid x \geq 0 , x \neq \frac { 7 } { 6 } \right\}$ 
B)  $( f / g ) ( x ) = \frac { 6 x - 7 } { \sqrt { x } } ;$ domain $\{ x \mid x \geq 0 \}$ 
C)  $( \mathrm { f } / \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 6 \mathrm { x } - 7 }$; domain $\{ x \mid x \neq 0 \}$ 
D)  $( \mathrm { f } / \mathrm { g } ) ( \mathrm { x } ) = \frac { \sqrt { \mathrm { x } } } { 6 \mathrm { x } - 7 } ;$ domain $\left\{ x \mid x \neq \frac { 7 } { 6 } \right\}$

Question 5

Identify which of the twelve basic functions listed below fit the description given.
-The one function that is decreasing from $( 0 , \infty )$

Accepted Answer

A)  $y = \frac { 1 } { x }$ 
B)  $y = | x |$ 
C)  $y = \ln x$ 
D)  $y = \frac { 1 } { 1 + e ^ { - x } }$ 
A)  $y = \frac { 1 } { x }$ 
B)  $y = | x |$ 
C)  $y = \ln x$ 
D)  $y = \frac { 1 } { 1 + e ^ { - x } }$

Question 6

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear
regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression.
-

Accepted Answer

A)  Linear regression 
B)  Quadratic regression 
C)  Cubic regression 
D)  Sinusoidal regression 
E)  Exponential regression 
A)  Linear regression 
B)  Quadratic regression 
C)  Cubic regression 
D)  Sinusoidal regression 
E)  Exponential regression

Question 7

Find the asymptote(s) of the given function.
-$f ( x ) = \frac { x - 7 } { x ^ { 2 } + 6 x }$ vertical asymptotes(s)

Accepted Answer

A)  $x = 6$ 
B)  $x = 0 , x = - 6$ 
C)  $x = - 6$ 
D)  $x = 7$ 
A)  $x = 6$ 
B)  $x = 0 , x = - 6$ 
C)  $x = - 6$ 
D)  $x = 7$

Question 8

Fill in the blanks to complete the statement.
-The graph of $y = 0.8 | - x | - 10$ can be obtained from the graph of $y = | x |$ by reflecting across the   -axis, shrinking vertically by a factor of    and then shifting   units in the ? direction   .

Accepted Answer

A)  $y ; - 0.8 ; 10$; downward 
B)  $x ; 10 ; 0.8$; upward 
C)  $x ; 0.8 ; 10$; downward 
D)  $\mathrm { y } ; 0.8 ; 10$; downward 
A)  $y ; - 0.8 ; 10$; downward 
B)  $x ; 10 ; 0.8$; upward 
C)  $x ; 0.8 ; 10$; downward 
D)  $\mathrm { y } ; 0.8 ; 10$; downward

Question 9

Perform the requested operation or operations. Find the domain of each.
-$$f ( x ) = 2 x + 7 , g ( x ) = 6 x ^ { 2 }$$
Find $( \mathrm { fg } ) ( \mathrm { x } )$.

Accepted Answer

A)  $12 x ^ { 3 } + 42 x ^ { 2 }$; domain: $( - \infty , \infty )$ 
B)  $12 x + 42$; domain: $( - \infty , \infty )$ 
C)  $6 x ^ { 2 } + 2 x + 7$; domain: $( - \infty , \infty )$ 
D)  $12 x ^ { 2 } + 42 x$; domain: $( - \infty , \infty )$ 
A)  $12 x ^ { 3 } + 42 x ^ { 2 }$; domain: $( - \infty , \infty )$ 
B)  $12 x + 42$; domain: $( - \infty , \infty )$ 
C)  $6 x ^ { 2 } + 2 x + 7$; domain: $( - \infty , \infty )$ 
D)  $12 x ^ { 2 } + 42 x$; domain: $( - \infty , \infty )$

Question 10

Solve the equation algebraically.
-$$x ( x - 5 ) = 14$$

Accepted Answer

A)  $- 2 ; 7$ 
B)  $0 ; 5$ 
C)  $2 ; - 7$ 
D)  $5 , - 14$ 
A)  $- 2 ; 7$ 
B)  $0 ; 5$ 
C)  $2 ; - 7$ 
D)  $5 , - 14$

Question 11

Perform the requested operation or operations.
-$$f ( x ) = x ^ { 2 } + 9 ; g ( x ) = \sqrt { x - 1 }$$
Find $g ( f ( x ) )$.

Accepted Answer

A)  $g ( f ( x ) ) = ( \sqrt { x - 1 } ) \left( x ^ { 2 } + 9 \right)$ 
B)  $g ( f ( x ) ) = \sqrt { x ^ { 2 } + 8 }$ 
C)  $g ( f ( x ) ) = \frac { \sqrt { x - 1 } } { x ^ { 2 } + 9 }$ 
D)  $g ( f ( x ) ) = x + 8$ 
A)  $g ( f ( x ) ) = ( \sqrt { x - 1 } ) \left( x ^ { 2 } + 9 \right)$ 
B)  $g ( f ( x ) ) = \sqrt { x ^ { 2 } + 8 }$ 
C)  $g ( f ( x ) ) = \frac { \sqrt { x - 1 } } { x ^ { 2 } + 9 }$ 
D)  $g ( f ( x ) ) = x + 8$

Question 12

Find two functions defined implicitly by the given relation.
-$3 x ^ { 2 } - y ^ { 2 } = 4$

Accepted Answer

A)  $y = \frac { x \sqrt { 3 } } { 2 }$ or $y = - \frac { x \sqrt { 3 } } { 2 }$ 
B)  $y = \sqrt { 3 } x - \sqrt { 4 }$ or $y = - \sqrt { 3 } x + \sqrt { 4 }$ 
C)  $y = \sqrt { 3 x ^ { 2 } - 4 }$ or $y = \sqrt { 3 x ^ { 2 } + 4 }$ 
D)  $y = \sqrt { 3 x ^ { 2 } - 4 }$ or $y = - \sqrt { 3 x ^ { 2 } - 4 }$ 
A)  $y = \frac { x \sqrt { 3 } } { 2 }$ or $y = - \frac { x \sqrt { 3 } } { 2 }$ 
B)  $y = \sqrt { 3 } x - \sqrt { 4 }$ or $y = - \sqrt { 3 } x + \sqrt { 4 }$ 
C)  $y = \sqrt { 3 x ^ { 2 } - 4 }$ or $y = \sqrt { 3 x ^ { 2 } + 4 }$ 
D)  $y = \sqrt { 3 x ^ { 2 } - 4 }$ or $y = - \sqrt { 3 x ^ { 2 } - 4 }$

Question 13

Choose the one alternative that best completes the statement or answers the question.
-For the graph shown, at which point does the function change from increasing to decreasing?

Accepted Answer

A)  $x = 0$ 
B)  $x = 2$ 
C)  $x = 2 / 3$ 
D)  $x = - 1.19$ 
A)  $x = 0$ 
B)  $x = 2$ 
C)  $x = 2 / 3$ 
D)  $x = - 1.19$

Question 14

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-$$y = ( x + 17 ) ^ { 2 }$$

Accepted Answer

A)  Shift the graph of $y = x ^ { 2 }$ down 17 units. 
B)  Shift the graph of $y = x ^ { 2 }$ up 17 units. 
C)  Shift the graph of $y = x ^ { 2 }$ right 17 units. 
D)  Shift the graph of $y = x ^ { 2 }$ left 17 units. 
A)  Shift the graph of $y = x ^ { 2 }$ down 17 units. 
B)  Shift the graph of $y = x ^ { 2 }$ up 17 units. 
C)  Shift the graph of $y = x ^ { 2 }$ right 17 units. 
D)  Shift the graph of $y = x ^ { 2 }$ left 17 units.

Question 15

Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of
these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the
graph of y1 across an axis.
-

Accepted Answer

A)  $f ( x ) = \sqrt { x - 6 }$ 
B)  $f ( x ) = \sqrt { x + 6 }$ 
C)  $f ( x ) = \sqrt { x } + 6$ 
D)  $f ( x ) = \sqrt { x } - 6$ 
A)  $f ( x ) = \sqrt { x - 6 }$ 
B)  $f ( x ) = \sqrt { x + 6 }$ 
C)  $f ( x ) = \sqrt { x } + 6$ 
D)  $f ( x ) = \sqrt { x } - 6$

Question 16

Find the asymptote(s) of the given function.
-$f ( x ) = \frac { x - 4 } { x ^ { 2 } + 1 }$ vertical asymptotes(s)

Accepted Answer

A)  None 
B)  $x = - 1$ 
C)  $x = 1$ 
D)  $x = 2 , x = - 2$ 
A)  None 
B)  $x = - 1$ 
C)  $x = 1$ 
D)  $x = 2 , x = - 2$

Question 17

Determine whether the graph is the graph of a function.
-

Accepted Answer

A) True 
 B)False

Question 18

Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is
removable or non-removable.
-$$f ( x ) = \frac { 4 } { x }$$

Accepted Answer

A) 
 
Yes; removable 
B) 
 
No 
C) 
 
No 
D)

Yes; non-removable 
A) 
 
Yes; removable 
B) 
 
No 
C) 
 
No 
D)

Yes; non-removable

Question 19

Match the numerical model to the corresponding model.
-$\begin{array}{r|rrrrrr}
\mathrm{x} & 3 & 4 & 5 & 6 & 7 & 8 \
\hline \mathrm{y} & 11 & 14 & 17 & 20 & 23 & 26
\end{array}$

Accepted Answer

A) 
  
B) 
  
C)

D) 
  
A) 
  
B) 
  
C)

D)

Question 20

Perform the requested operation or operations.
-$$f ( x ) = \frac { 1 } { x - 6 } ; g ( x ) = \sqrt { x }$$
Find $f ( g ( x ) )$.

Accepted Answer

A)  $f ( g ( x ) ) = ( x - 6 ) \sqrt { x }$ 
B)  $f ( g ( x ) ) = \frac { \sqrt { x } } { x - 6 }$ 
C)  $f ( g ( x ) ) = \frac { 1 } { \sqrt { x } - 6 }$ 
D)  $f ( g ( x ) ) = \sqrt { \frac { 1 } { x - 6 } }$ 
A)  $f ( g ( x ) ) = ( x - 6 ) \sqrt { x }$ 
B)  $f ( g ( x ) ) = \frac { \sqrt { x } } { x - 6 }$ 
C)  $f ( g ( x ) ) = \frac { 1 } { \sqrt { x } - 6 }$ 
D)  $f ( g ( x ) ) = \sqrt { \frac { 1 } { x - 6 } }$

Find the asymptote(s) of the given function. - $f ( x ) = \frac { x - 3 } { x ^ { 2 } - 36 }$ vertical asymptotes(s)

Perform the requested operation or operations. Find the domain of each. - $f ( x ) = \sqrt { x } ; g ( x ) = 6 x - 7$ Find $f / g$ .

Identify which of the twelve basic functions listed below fit the description given. -The one function that is decreasing from $( 0 , \infty )$

Tell which of the following types of regression is likely to give the most accurate model for the scatter plot shown: linear regression, quadratic regression, cubic regression, exponential regression, sinusoidal regression. -

Find the asymptote(s) of the given function. - $f ( x ) = \frac { x - 7 } { x ^ { 2 } + 6 x }$ vertical asymptotes(s)

Perform the requested operation or operations. Find the domain of each. - $f ( x ) = 2 x + 7 , g ( x ) = 6 x ^ { 2 }$ Find $( \mathrm { fg } ) ( \mathrm { x } )$ .

Solve the equation algebraically. - $x ( x - 5 ) = 14$

Perform the requested operation or operations. - $f ( x ) = x ^ { 2 } + 9 ; g ( x ) = \sqrt { x - 1 }$ Find $g ( f ( x ) )$ .

Find two functions defined implicitly by the given relation. - $3 x ^ { 2 } - y ^ { 2 } = 4$

Choose the one alternative that best completes the statement or answers the question. -For the graph shown, at which point does the function change from increasing to decreasing?

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - $y = ( x + 17 ) ^ { 2 }$

Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the graph of y1 across an axis. -

Find the asymptote(s) of the given function. - $f ( x ) = \frac { x - 4 } { x ^ { 2 } + 1 }$ vertical asymptotes(s)

Determine whether the graph is the graph of a function. -

Match the numerical model to the corresponding model. - 3 4 5 6 7 8 11 14 17 20 23 26

Perform the requested operation or operations. - $f ( x ) = \frac { 1 } { x - 6 } ; g ( x ) = \sqrt { x }$ Find $f ( g ( x ) )$ .

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 1: Functions and Graphs

Find the asymptote(s) of the given function. - f(x)=x−3x2−36f ( x ) = \frac { x - 3 } { x ^ { 2 } - 36 }f(x)=x2−36x−3​ vertical asymptotes(s)

Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - g(x)=x2−3xxg ( x ) = \frac { x ^ { 2 } - 3 x } { x }g(x)=xx2−3x​

Perform the requested operation or operations. Find the domain of each. - f(x)=x;g(x)=6x−7f ( x ) = \sqrt { x } ; g ( x ) = 6 x - 7f(x)=x​;g(x)=6x−7 Find f/gf / gf/g .

Identify which of the twelve basic functions listed below fit the description given. -The one function that is decreasing from (0,∞)( 0 , \infty )(0,∞)