Question 1

The graph of a function f is given. Use the graph to answer the question.
-For what numbers x is f(x) > 0?

Accepted Answer

A)  $( - 60 , \infty )$ 
B)  $( - \infty - 60 )$ 
C)  $[ - 100 , - 60 ) , ( 70,100 )$ 
D)  $( - 60,70 )$ 
A)  $( - 60 , \infty )$ 
B)  $( - \infty - 60 )$ 
C)  $[ - 100 , - 60 ) , ( 70,100 )$ 
D)  $( - 60,70 )$

Question 2

Choose the one alternative that best completes the statement or answers the question.
Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=(x-5)^{2}$
 
 A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 3

The graph of a function f is given. Use the graph to answer the question.
-Is f(8) positive or negative?

Accepted Answer

A)  positive 
B)  negative 
A)  positive 
B)  negative

Question 4

Graph the function.
-$$f ( x ) = x$$
 
 A)

Accepted Answer

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

Question 5

Determine algebraically whether the function is even, odd, or neither.
-$f ( x ) = - 4 x ^ { 2 } + 8$

Accepted Answer

A)  even 
B)  odd 
C)  neither 
A)  even 
B)  odd 
C)  neither

Question 6

Find the value for the function.
-Find $f ( 2 x )$ when $f ( x ) = - 2 x ^ { 2 } - 3 x + 1$

Accepted Answer

A)  $- 8 x ^ { 2 } - 6 x + 1$ 
B)  $- 8 x ^ { 2 } - 6 x + 2$ 
C)  $- 4 x ^ { 2 } - 6 x + 2$ 
D)  $- 4 x ^ { 2 } - 6 x + 1$ 
A)  $- 8 x ^ { 2 } - 6 x + 1$ 
B)  $- 8 x ^ { 2 } - 6 x + 2$ 
C)  $- 4 x ^ { 2 } - 6 x + 2$ 
D)  $- 4 x ^ { 2 } - 6 x + 1$

Question 7

Match the correct function to the graph.
-  A) $y = | 1 - x |$

Accepted Answer

B)  $y = | x + 2 |$ 
C)  $y = x - 2$ 
D)  $y = | 2 - x |$ 
B)  $y = | x + 2 |$ 
C)  $y = x - 2$ 
D)  $y = | 2 - x |$

Question 8

For the function, find the average rate of change of f from 1 to x: $$\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$$
-$$f ( x ) = \frac { 6 } { x + 5 }$$

Accepted Answer

A)  $- \frac { 1 } { x + 5 }$ 
B)  $\frac { 6 } { ( x - 1 ) ( x + 5 ) }$ 
C)  $\frac { 6 } { x ( x + 5 ) }$ 
D)  $\frac { 1 } { x + 5 }$ 
A)  $- \frac { 1 } { x + 5 }$ 
B)  $\frac { 6 } { ( x - 1 ) ( x + 5 ) }$ 
C)  $\frac { 6 } { x ( x + 5 ) }$ 
D)  $\frac { 1 } { x + 5 }$

Question 9

Solve the problem.
-If $f ( x ) = 9 x ^ { 3 } + 5 x ^ { 2 } - x + C$ and $f ( - 2 ) = 1$, what is the value of $C$ ?

Accepted Answer

A)  $C = - 53$ 
B)  $C = - 13$ 
C)  $\mathrm { C } = 51$ 
D)  $C = - 93$ 
A)  $C = - 53$ 
B)  $C = - 13$ 
C)  $\mathrm { C } = 51$ 
D)  $C = - 93$

Question 10

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists.
-

Accepted Answer

A)  Absolute maximum: none; Absolute minimum: none 
B)  Absolute maximum: none; Absolute minimum: $f ( 1 ) = 2$ 
C)  Absolute maximum: $f ( - 1 ) = 6$; Absolute minimum: $f ( 1 ) = 2$ 
D)  Absolute maximum: $f ( 3 ) = 5$; Absolute minimum: $f ( 1 ) = 2$ 
A)  Absolute maximum: none; Absolute minimum: none 
B)  Absolute maximum: none; Absolute minimum: $f ( 1 ) = 2$ 
C)  Absolute maximum: $f ( - 1 ) = 6$; Absolute minimum: $f ( 1 ) = 2$ 
D)  Absolute maximum: $f ( 3 ) = 5$; Absolute minimum: $f ( 1 ) = 2$

Question 11

The graph of a function f is given. Use the graph to answer the question.
-Find the numbers, if any, at which f has a local minimum. What are the local minima?

Accepted Answer

A)  f has a local minimum at x = 0; the local minimum is 3 
B)  f has a local minimum at x = -2 and 2; the local minimum is 0 
C)  f has a local minimum at x = -2; the local minimum is 0 
D)  f has no local minimum 
A)  f has a local minimum at x = 0; the local minimum is 3 
B)  f has a local minimum at x = -2 and 2; the local minimum is 0 
C)  f has a local minimum at x = -2; the local minimum is 0 
D)  f has no local minimum

Question 12

Write the word or phrase that best completes each statement or answers the question.
-An electric company has the following rate schedule for electricity usage in single-family residences: $$\begin{array} { l l } 
\text { Monthly service charge } & \$ 4.93 \
\text { Per kilowatt service charge}\
\text { 1st }  \text { 300  kilowatts } & (\$ 0.11589 / \mathrm { kW } \

\text { Over 300   kilowatts } &    (\$ 0.13321 / \mathrm { kW }
\end{array}$$ What is the charge for using 300 kilowatts in one month?
What is the charge for using 375 kilowatts in one month?
Construct a function that gives the monthly charge C for x kilowatts of electricity.

Accepted Answer

\[\begin{array} { l } 
\$ 39.70 \
\$ 49

Question 13

Find the value for the function.
-$\text { Find } f(-x) \text { when } f(x)=2 x^{2}+3 x-2$

Accepted Answer

A)  $2 x^{2}-3 x+2$ 
B)  $2 x^{2}-3 x-2$ 
C)  $-2 x^{2}-3 x+2$ 
D)  $-2 x^{2}-3 x-2$ 
A)  $2 x^{2}-3 x+2$ 
B)  $2 x^{2}-3 x-2$ 
C)  $-2 x^{2}-3 x+2$ 
D)  $-2 x^{2}-3 x-2$

Question 14

Find the domain of the function.
-$$f ( x ) = x ^ { 2 } + 2$$

Accepted Answer

A)  $\{ x \mid x > - 2 \}$ 
B)  $\{ x \mid x z - 2 \}$ 
C)  all real numbers 
D)  $\{ x \mid x \geq - 2 \}$ 
A)  $\{ x \mid x > - 2 \}$ 
B)  $\{ x \mid x z - 2 \}$ 
C)  all real numbers 
D)  $\{ x \mid x \geq - 2 \}$

Question 15

Determine whether the equation defines y as a function of x.
-$y=\frac{5 x+3}{x+2}$

Accepted Answer

A)  function 
B)  not a function 
A)  function 
B)  not a function

Question 16

Solve the problem.
-A farmer's silo is the shape of a cylinder with a hemisphere as the roof. If the height of the silo is 66 feet and the radius of the hemisphere is r feet, express the volume of the silo as a function of r. A) $V ( r ) = \pi ( 66 - r ) r ^ { 2 } + \frac { 2 } { 3 } \pi r ^ { 3 }$

Accepted Answer

B)  $\mathrm { V } ( \mathrm { r } ) = \pi ( 66 - \mathrm { r } ) + \frac { 4 } { 3 } \pi \mathrm { r } ^ { 2 }$ 
C)  $V ( r ) = \pi ( 66 - r ) r ^ { 3 } + \frac { 4 } { 3 } \pi r ^ { 2 }$ 
D)  $V ( r ) = 66 \pi r ^ { 2 } + \frac { 8 } { 3 } \pi r ^ { 3 }$ 
B)  $\mathrm { V } ( \mathrm { r } ) = \pi ( 66 - \mathrm { r } ) + \frac { 4 } { 3 } \pi \mathrm { r } ^ { 2 }$ 
C)  $V ( r ) = \pi ( 66 - r ) r ^ { 3 } + \frac { 4 } { 3 } \pi r ^ { 2 }$ 
D)  $V ( r ) = 66 \pi r ^ { 2 } + \frac { 8 } { 3 } \pi r ^ { 3 }$

Question 17

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two
decimal places.
-$f(x)=x^{3}-3 x+3,(-2,2)$

Accepted Answer

A) 
local maximum at $ (1,1) $
 local minimum at $ (-1,5) $ 
increasing on $ (-2,-1) $
 decreasing on $ (-1,1) $ 
B)  local maximum at $ (-1,5) $
local minimum at $ (1,1) $
increasing on $ (-2,-1) $ and $ (1,2) $
decreasing on $ (-1,1) $ 
C)  local maximum at $ (1,1) $
local minimum at $ (-1,5) $
increasing on $ (-2,-1) $ and $ (1,2) $
decreasing on $ (-1,1) $ 
D)  
$\begin{array}{l}
\text { local maximum at }(-1,5) \
\text { local minimum at }(1,1) \
\text { increasing on }(-1,1) \
\text { decreasing on }(-2,-1) \text { and }(1,2)
\end{array}$ 
A) 
local maximum at $ (1,1) $
 local minimum at $ (-1,5) $ 
increasing on $ (-2,-1) $
 decreasing on $ (-1,1) $ 
B)  local maximum at $ (-1,5) $
local minimum at $ (1,1) $
increasing on $ (-2,-1) $ and $ (1,2) $
decreasing on $ (-1,1) $ 
C)  local maximum at $ (1,1) $
local minimum at $ (-1,5) $
increasing on $ (-2,-1) $ and $ (1,2) $
decreasing on $ (-1,1) $ 
D)  
$\begin{array}{l}
\text { local maximum at }(-1,5) \
\text { local minimum at }(1,1) \
\text { increasing on }(-1,1) \
\text { decreasing on }(-2,-1) \text { and }(1,2)
\end{array}$

Question 18

Solve the problem.
-$$\text { If } f ( x ) = \operatorname { int } ( 4 x ) \text {, find } f ( 1.8 )$$

Accepted Answer

A)  8 
B)  1 
C)  7 
D)  2 
A)  8 
B)  1 
C)  7 
D)  2

Question 19

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = \frac { 7 x - 6 } { 6 x - 1 } ; g ( x ) = \frac { 4 x } { 6 x - 1 }$$
Find $f + g$.

Accepted Answer

A)  $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } \right\}$ 
B)  $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \{ x \mid x \neq 0 \}$ 
C)  $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } , x \neq \frac { 6 } { 11 } \right\}$ 
D)  $( f + g ) ( x ) = \frac { 3 x + 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } \right\}$ 
A)  $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } \right\}$ 
B)  $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \{ x \mid x \neq 0 \}$ 
C)  $( f + g ) ( x ) = \frac { 11 x - 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } , x \neq \frac { 6 } { 11 } \right\}$ 
D)  $( f + g ) ( x ) = \frac { 3 x + 6 } { 6 x - 1 } ; \left\{ x \mid x \neq \frac { 1 } { 6 } \right\}$

Question 20

Solve the problem.
-Given $f ( x ) = \frac { 1 } { x }$ and $\left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x }$, find the function $g$.

Accepted Answer

A)  $g ( x ) = \frac { x - 6 } { x - 4 }$ 
B)  $g ( x ) = \frac { x + 6 } { x + 4 }$

$C ) g ( x ) = \frac { x - 4 } { x - 6 }$ 
D)  $g ( x ) = \frac { x + 4 } { x + 6 }$ 
A)  $g ( x ) = \frac { x - 6 } { x - 4 }$ 
B)  $g ( x ) = \frac { x + 6 } { x + 4 }$

$C ) g ( x ) = \frac { x - 4 } { x - 6 }$ 
D)  $g ( x ) = \frac { x + 4 } { x + 6 }$

The graph of a function f is given. Use the graph to answer the question. -For what numbers x is f(x) > 0?

The graph of a function f is given. Use the graph to answer the question. -Is f(8) positive or negative?

Graph the function. - $f ( x ) = x$ A) B) C) D)

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = - 4 x ^ { 2 } + 8$

Find the value for the function. -Find $f ( 2 x )$ when $f ( x ) = - 2 x ^ { 2 } - 3 x + 1$

Match the correct function to the graph. - A) $y = | 1 - x |$ B) $y = | x + 2 |$ C) $y = x - 2$ D) $y = | 2 - x |$

For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = \frac { 6 } { x + 5 }$

Solve the problem. -If $f ( x ) = 9 x ^ { 3 } + 5 x ^ { 2 } - x + C$ and $f ( - 2 ) = 1$ , what is the value of $C$ ?

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. -

The graph of a function f is given. Use the graph to answer the question. -Find the numbers, if any, at which f has a local minimum. What are the local minima?

Find the value for the function. - $\text { Find } f(-x) \text { when } f(x)=2 x^{2}+3 x-2$

Find the domain of the function. - $f ( x ) = x ^ { 2 } + 2$

Determine whether the equation defines y as a function of x. - $y=\frac{5 x+3}{x+2}$

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two decimal places. - $f(x)=x^{3}-3 x+3,(-2,2)$

Solve the problem. - $\text { If } f ( x ) = \operatorname { int } ( 4 x ) \text {, find } f ( 1.8 )$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \frac { 7 x - 6 } { 6 x - 1 } ; g ( x ) = \frac { 4 x } { 6 x - 1 }$ Find $f + g$ .

Solve the problem. -Given $f ( x ) = \frac { 1 } { x }$ and $\left( \frac { f } { g } \right) ( x ) = \frac { x - 4 } { x ^ { 2 } - 6 x }$ , find the function $g$ .

Linear and Quadratic Functions

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 1: Functions and Their Graphs

The graph of a function f is given. Use the graph to answer the question. -For what numbers x is f(x) > 0?

Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - f(x)=(x−5)2f(x)=(x-5)^{2}f(x)=(x−5)2 A) B) C) D)