Question 1

Find the inverse of the function.
-$$f ( x ) = 8 x ^ { 3 } - 7$$

Accepted Answer

A)  Not a one-to-one function 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } } { 8 } } + 7$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } - 7 } { 8 } }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } + 7 } { 8 } }$ 
A)  Not a one-to-one function 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } } { 8 } } + 7$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } - 7 } { 8 } }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt [ 3 ] { \frac { \mathrm { x } + 7 } { 8 } }$

Question 2

Identify which of the twelve basic functions listed below fit the description given.
-The three functions that are bounded above

Accepted Answer

A)  $y = \ln x , y = \sqrt { x } , y = \frac { 1 } { 1 + e ^ { - x } }$ 
B)  $y = \sin x , y = \cos x , y = \operatorname { int } ( x )$ 
C)  $y = \sin x , y = \cos x , y = \frac { 1 } { 1 + e ^ { - x } }$ 
D)  $y = \sin x , y = \cos x , y = \ln x$ 
A)  $y = \ln x , y = \sqrt { x } , y = \frac { 1 } { 1 + e ^ { - x } }$ 
B)  $y = \sin x , y = \cos x , y = \operatorname { int } ( x )$ 
C)  $y = \sin x , y = \cos x , y = \frac { 1 } { 1 + e ^ { - x } }$ 
D)  $y = \sin x , y = \cos x , y = \ln x$

Question 3

Fill in the blanks to complete the statement.
-The graph of $y = ( x - 8 ) ^ { 2 } - 5$ can be obtained from the graph of $y = x ^ { 2 }$ by shifting horizontally ? units to the $\underline { ? }$ and shifting vertically ? units to the ? direction.

Accepted Answer

A)  8 ; left; 5; upward 
B)  8; left; 5; downward 
C)  8 ; right; 5 ; downward 
D)  5 ; right; 8; downward 
A)  8 ; left; 5; upward 
B)  8; left; 5; downward 
C)  8 ; right; 5 ; downward 
D)  5 ; right; 8; downward

Question 4

Find a direct relationship between x and y.
-$x = 3 t$ and $y = 5 t + 5$

Accepted Answer

A)  $y = \frac { x } { 3 }$ 
B)  $y = \frac { 5 } { 3 } x + 5$ 
C)  $y = 15 x + 5$ 
D)  $y = 15 x$ 
A)  $y = \frac { x } { 3 }$ 
B)  $y = \frac { 5 } { 3 } x + 5$ 
C)  $y = 15 x + 5$ 
D)  $y = 15 x$

Question 5

Solve the problem.
-Use the graph of $f$ to estimate the local maximum and local minimum.

Accepted Answer

A)  Local maximum: 0; local minimum: $- 4$ 
B)  No local maximum; local minimum: $- 4$ 
C)  Local maximum: $\infty$; local minima: $- 2$ and 2 
D)  Local maximum: 0; local minima: $- 2$ and 2 
A)  Local maximum: 0; local minimum: $- 4$ 
B)  No local maximum; local minimum: $- 4$ 
C)  Local maximum: $\infty$; local minima: $- 2$ and 2 
D)  Local maximum: 0; local minima: $- 2$ and 2

Question 6

Find the inverse of the function.
-$$f ( x ) = \frac { 8 } { x + 2 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x } { 2 + 8 x }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 2 + 8 \mathrm { x } } { \mathrm { x } }$ 
C)  $f ^ { - 1 } ( x ) = \frac { - 2 x + 8 } { x }$ 
D)  Not invertible 
A)  $f ^ { - 1 } ( x ) = \frac { x } { 2 + 8 x }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 2 + 8 \mathrm { x } } { \mathrm { x } }$ 
C)  $f ^ { - 1 } ( x ) = \frac { - 2 x + 8 } { x }$ 
D)  Not invertible

Question 7

Choose the one alternative that best completes the statement or answers the question.
Graph the piecewise-defined function.
-$$g ( x ) = \left\{ \begin{array} { l l } 
\frac { 1 } { x } & \text { if } x < 0 \
e ^ { x } & \text { if } x \geq 0
\end{array} \right.$$

Accepted Answer

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

Question 8

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

Accepted Answer

A)  $y = 7$ 
B)  $y = 0$ 
C)  None 
D)  $y = - 2$ 
A)  $y = 7$ 
B)  $y = 0$ 
C)  None 
D)  $y = - 2$

Question 9

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

Question 10

Match the function with the graph.
-

Accepted Answer

A)  $y = - \cos x$ 
B)  $y = \cos x$ 
C)  $y = - \sin x$ 
D)  $y = \sin x$ 
A)  $y = - \cos x$ 
B)  $y = \cos x$ 
C)  $y = - \sin x$ 
D)  $y = \sin x$

Question 11

Choose the one alternative that best completes the statement or answers the question.
Graph the piecewise-defined function.
-$$f ( x ) = \left\{ \begin{array} { l } 
\sin x \text { if } x \leq 0 \
| x | \text { if } x > 0
\end{array} \right.$$

Accepted Answer

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

Question 12

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)  $f ( x ) = \sqrt { - x + 4 }$ 
B)  $f ( x ) = \sqrt { - x } + 4$ 
C)  $f ( x ) = - \sqrt { x } + 4$ 
D)  $f ( x ) = - \sqrt { x + 4 }$ 
A)  $f ( x ) = \sqrt { - x + 4 }$ 
B)  $f ( x ) = \sqrt { - x } + 4$ 
C)  $f ( x ) = - \sqrt { x } + 4$ 
D)  $f ( x ) = - \sqrt { x + 4 }$

Question 13

Solve the problem.
-Some of the results of an analysis, on the makeup of garbage, are given in the following table. The table displays various years which gives the number of pounds per person per day of various types of waste materials.

For paper, calculate the average rates of change between consecutive data points in the table. Interpret the meani your results.

Accepted Answer

A)  The rate of increase slows down during the 1980's, but then increases during the 1990's and 2000-2008. 
B)  The rate of increase slows down during the 1990's, but then increases during 2000-2008. 
C)  The rate of increase increases during the 1990 's, but then decreases during 2000-2008. 
D)  The rate of increase stays the same from the 1980's through 2000-2008. 
A)  The rate of increase slows down during the 1980's, but then increases during the 1990's and 2000-2008. 
B)  The rate of increase slows down during the 1990's, but then increases during 2000-2008. 
C)  The rate of increase increases during the 1990 's, but then decreases during 2000-2008. 
D)  The rate of increase stays the same from the 1980's through 2000-2008.

Question 14

Find the domain of the given function.
-$$f ( x ) = \sqrt { 2 - x }$$

Accepted Answer

A)  All real numbers 
B)  $( - \infty , 2 ) \cup ( 2 , \infty )$ 
C)  $( \sqrt { 2 } , \infty )$ 
D)  $( - \infty , 2 ]$ 
A)  All real numbers 
B)  $( - \infty , 2 ) \cup ( 2 , \infty )$ 
C)  $( \sqrt { 2 } , \infty )$ 
D)  $( - \infty , 2 ]$

Question 15

Describe how to transform the graph of f into the graph of g.
-$$f ( x ) = \sqrt { x } \text { and } g ( x ) = - \sqrt { - x }$$

Accepted Answer

A)  The two graphs are the same. 
B)  Reflect the graph of $f$ across the $y$-axis. 
C)  Reflect the graph of $f$ across the $x$-axis. 
D)  Reflect the graph of $\mathrm { f }$ across the $y$-axis and then reflect across the $x$-axis. 
A)  The two graphs are the same. 
B)  Reflect the graph of $f$ across the $y$-axis. 
C)  Reflect the graph of $f$ across the $x$-axis. 
D)  Reflect the graph of $\mathrm { f }$ across the $y$-axis and then reflect across the $x$-axis.

Question 16

Determine algebraically whether the function is even, odd, or neither even nor odd.
-$$f ( x ) = - 0.91 x ^ { 2 } + | x | + 6$$

Accepted Answer

A)  Neither 
B)  Odd 
C)  Even 
A)  Neither 
B)  Odd 
C)  Even

Question 17

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-$$y = ( x - 20 ) ^ { 2 } + 11$$

Accepted Answer

A)  Shift the graph of $y = x ^ { 2 }$ left 20 units and then down 11 units. 
B)  Shift the graph of $y = x ^ { 2 }$ up 20 units and then right 11 units. 
C)  Shift the graph of $y = x ^ { 2 }$ right 20 units and then up 11 units. 
D)  Shift the graph of $y = x ^ { 2 }$ left 20 units and then up 11 units. 
A)  Shift the graph of $y = x ^ { 2 }$ left 20 units and then down 11 units. 
B)  Shift the graph of $y = x ^ { 2 }$ up 20 units and then right 11 units. 
C)  Shift the graph of $y = x ^ { 2 }$ right 20 units and then up 11 units. 
D)  Shift the graph of $y = x ^ { 2 }$ left 20 units and then up 11 units.

Question 18

Write the word or phrase that best completes each statement or answers the question.
Graph the function on your calculator in order to answer the following questions:
On what intervals is the function increasing? decreasing?
Is the function odd, even, or neither?
Give the function's extrema, if any.
Find the horizontal asymptotes, if any.
How does the graph relate to a graph of one of the twelve basic functions?
-$$f ( x ) = - \frac { 1 } { 1 + e ^ { - x } }$$

Accepted Answer

Decreasing on @#LAT-DLM&
Neither odd nor

Question 19

Perform the requested operation or operations. Find the domain of each.
-$f ( x ) = \sqrt { x + 8 }$ and $g ( x ) = | x - 6 |$
Find $f g$.

Accepted Answer

A)  $| x - 6 | \sqrt { x + 8 } ;$ domain: $( 6 , \infty )$ 
B)  $\sqrt { x ^ { 2 } + 2 x - 48 }$; domain: $( - \infty , - 8 ) \cup ( 6 , \infty )$ 
C)  $\left| x ^ { 2 } + 2 x - 48 \right|$; domain: $( - \infty , \infty )$ 
D)  $| x - 6 | \sqrt { x + 8 }$; domain: $( - 8 , \infty )$ 
A)  $| x - 6 | \sqrt { x + 8 } ;$ domain: $( 6 , \infty )$ 
B)  $\sqrt { x ^ { 2 } + 2 x - 48 }$; domain: $( - \infty , - 8 ) \cup ( 6 , \infty )$ 
C)  $\left| x ^ { 2 } + 2 x - 48 \right|$; domain: $( - \infty , \infty )$ 
D)  $| x - 6 | \sqrt { x + 8 }$; domain: $( - 8 , \infty )$

Question 20

Determine if the function is one-to-one.
-

Accepted Answer

A) True 
 B)False

Find the inverse of the function. - $f ( x ) = 8 x ^ { 3 } - 7$

Identify which of the twelve basic functions listed below fit the description given. -The three functions that are bounded above

Fill in the blanks to complete the statement. -The graph of $y = ( x - 8 ) ^ { 2 } - 5$ can be obtained from the graph of $y = x ^ { 2 }$ by shifting horizontally ? units to the $\underline { ? }$ and shifting vertically ? units to the ? direction.

Find a direct relationship between x and y. - $x = 3 t$ and $y = 5 t + 5$

Solve the problem. -Use the graph of $f$ to estimate the local maximum and local minimum.

Find the inverse of the function. - $f ( x ) = \frac { 8 } { x + 2 }$

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

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. -

Match the function with the graph. -

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 domain of the given function. - $f ( x ) = \sqrt { 2 - x }$

Describe how to transform the graph of f into the graph of g. - $f ( x ) = \sqrt { x } \text { and } g ( x ) = - \sqrt { - x }$

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = - 0.91 x ^ { 2 } + | x | + 6$

Choose the one alternative that best completes the statement or answers the question. Solve the problem. - $y = ( x - 20 ) ^ { 2 } + 11$

Perform the requested operation or operations. Find the domain of each. - $f ( x ) = \sqrt { x + 8 }$ and $g ( x ) = | x - 6 |$ Find $f g$ .

Determine if the function is one-to-one. -

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 inverse of the function. - f(x)=8x3−7f ( x ) = 8 x ^ { 3 } - 7f(x)=8x3−7