Question 1

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-$$f ( x ) = \frac { 1 } { 7 x }$$

Accepted Answer

A)  $\frac { - 1 } { 7 x ( x + h ) }$ 
B)  $\frac { 1 } { 7 x }$ 
C)  0 
D)  $\frac { - 1 } { x ( x + h ) }$ 
A)  $\frac { - 1 } { 7 x ( x + h ) }$ 
B)  $\frac { 1 } { 7 x }$ 
C)  0 
D)  $\frac { - 1 } { x ( x + h ) }$

Question 2

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. If necessary, round answers to two decimal places.
-$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 1 ; ( - 5,5 )$$

Accepted Answer

A)  local minimum at $( 2 , - 3 )$ 
B)  local maximum at $( 0,1 )$ local minimum at $( 2 , - 3 )$ 
C)  local minimum at $( 0,1 )$ 
D)  none
local maximum at $( 2 , - 3 )$ 
A)  local minimum at $( 2 , - 3 )$ 
B)  local maximum at $( 0,1 )$ local minimum at $( 2 , - 3 )$ 
C)  local minimum at $( 0,1 )$ 
D)  none
local maximum at $( 2 , - 3 )$

Question 3

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-$$( - 1,0 )$$

Accepted Answer

A)  constant 
B)  decreasing 
C)  increasing 
A)  constant 
B)  decreasing 
C)  increasing

Question 4

Find the function.
-Find the function that is finally graphed after the following transformations are applied to the graph of $$\mathrm { y } = | \mathrm { x } |$$ The graph is shifted right 3 units, stretched by a factor of 3, shifted vertically down 2 units, and finally reflected across the x-axis. A) $y = - ( 3 | x + 3 | - 2 )$

Accepted Answer

B)  $y = - ( 3 | x - 3 | - 2 )$ 
C)  $y = - 3 | x - 3 | - 2$ 
D)  $y = 3 | - x - 3 | - 2$ 
B)  $y = - ( 3 | x - 3 | - 2 )$ 
C)  $y = - 3 | x - 3 | - 2$ 
D)  $y = 3 | - x - 3 | - 2$

Question 5

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.
-$$f ( x ) = \frac { 1 } { x + 5 }$$
 
 A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 6

The graph of a function f is given. Use the graph to answer the question.
-How often does the line y = 20 intersect the graph?

Accepted Answer

A)  once 
B)  twice 
C)  three times 
D)  does not intersect 
A)  once 
B)  twice 
C)  three times 
D)  does not intersect

Question 7

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$$f ( x ) = - \frac { 1 } { x }$$
 
 A)

Accepted Answer

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

Question 8

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function.
-The reflection of the graph of y = f(x) across the x-axis

Accepted Answer

A)  (2, -4) 
B)  (-2, 4) 
C)  (2, 4) 
D)  (-2, -4) 
A)  (2, -4) 
B)  (-2, 4) 
C)  (2, 4) 
D)  (-2, -4)

Question 9

The graph of a function is given. Decide whether it is even, odd, or neither.
-

Accepted Answer

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

Question 10

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = 2 x + 5 ; g ( x ) = 6 x - 1$$
Find $\frac { f } { g }$.

Accepted Answer

A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 2 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 6 } \right\}$ 
B)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 2 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq - \frac { 5 } { 2 } \right\}$ 
C)  $\left( \frac { f } { g } \right) ( x ) = \frac { 6 x - 1 } { 2 x + 5 } ; \left\{ x \mid x \neq - \frac { 5 } { 2 } \right\}$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 6 \mathrm { x } - 1 } { 2 \mathrm { x } + 5 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 6 } \right\}$ 
A)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 2 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 6 } \right\}$ 
B)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 2 \mathrm { x } + 5 } { 6 \mathrm { x } - 1 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq - \frac { 5 } { 2 } \right\}$ 
C)  $\left( \frac { f } { g } \right) ( x ) = \frac { 6 x - 1 } { 2 x + 5 } ; \left\{ x \mid x \neq - \frac { 5 } { 2 } \right\}$ 
D)  $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } ) = \frac { 6 \mathrm { x } - 1 } { 2 \mathrm { x } + 5 } ; \left\{ \mathrm { x } \mid \mathrm { x } \neq \frac { 1 } { 6 } \right\}$

Question 11

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = 16 - x ^ { 2 } ; g ( x ) = 4 - x$$
Find $f + g$.

Accepted Answer

A)  $( f + g ) ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 16 x + 64$; all real numbers 
B)  $( f + g ) ( x ) = - x ^ { 2 } - x + 20 ; \{ x \mid x \neq 4 , x \neq - 5 \}$ 
C)  $( f + g ) ( x ) = 4 + x ; \{ x \mid x \neq - 4 \}$ 
D)  $( f + g ) ( x ) = - x ^ { 2 } + x + 12$; all real numbers 
A)  $( f + g ) ( x ) = x ^ { 3 } - 4 x ^ { 2 } - 16 x + 64$; all real numbers 
B)  $( f + g ) ( x ) = - x ^ { 2 } - x + 20 ; \{ x \mid x \neq 4 , x \neq - 5 \}$ 
C)  $( f + g ) ( x ) = 4 + x ; \{ x \mid x \neq - 4 \}$ 
D)  $( f + g ) ( x ) = - x ^ { 2 } + x + 12$; all real numbers

Question 12

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.
-$f(x)=(x+2)^{3}$
 
 A)

Accepted Answer

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

Question 13

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=-(x+3)^{2}-2$
 
 A)

Accepted Answer

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

Question 14

Find the average rate of change for the function between the given values.
-$f ( x ) = - 3 x ^ { 2 } - x$; from 5 to 6

Accepted Answer

A)  $- 34$ 
B)  $- \frac { 1 } { 6 }$ 
C)  $- 2$ 
D)  $\frac { 1 } { 2 }$ 
A)  $- 34$ 
B)  $- \frac { 1 } { 6 }$ 
C)  $- 2$ 
D)  $\frac { 1 } { 2 }$

Question 15

Graph the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
x - 1 & \text { if } x < 1 \
- 5 & \text { if } x \geq 1
\end{array} \right.$$

A)

Accepted Answer

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

Question 16

Find the value for the function.
-Find $f ( 2 x )$ when $f ( x ) = \sqrt { 2 x ^ { 2 } - 7 x }$.

Accepted Answer

A)  $\sqrt { 4 x ^ { 2 } - 14 x }$ 
B)  $\sqrt { 4 x ^ { 2 } - 28 x }$ 
C)  $\sqrt { 8 x ^ { 2 } - 14 x }$ 
D)  $2 \sqrt { 2 x ^ { 2 } - 7 x }$ 
A)  $\sqrt { 4 x ^ { 2 } - 14 x }$ 
B)  $\sqrt { 4 x ^ { 2 } - 28 x }$ 
C)  $\sqrt { 8 x ^ { 2 } - 14 x }$ 
D)  $2 \sqrt { 2 x ^ { 2 } - 7 x }$

Question 17

For the given functions f and g, find the requested function and state its domain.
-$$f ( x ) = 7 x + 3 ; g ( x ) = 3 x + 7$$
Find f $\cdot g .$

Accepted Answer

A)  $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 21 ; \{ x \mid x \neq 21 \}$ 
B)  $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 58 x + 21$; all real numbers 
C)  $( f \cdot g ) ( x ) = 10 x ^ { 2 } + 58 x + 10$; all real numbers 
D)  $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 16 x + 21 ; \{ x \mid x \neq 21 \}$ 
A)  $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 21 ; \{ x \mid x \neq 21 \}$ 
B)  $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 58 x + 21$; all real numbers 
C)  $( f \cdot g ) ( x ) = 10 x ^ { 2 } + 58 x + 10$; all real numbers 
D)  $( f \cdot g ) ( x ) = 21 x ^ { 2 } + 16 x + 21 ; \{ x \mid x \neq 21 \}$

Question 18

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.
-$$f ( x ) = x ^ { 5 } - x ^ { 2 } ; ( - 2,2 )$$

Accepted Answer

local maximum at (0, 0)
local

Question 19

The graph of a function is given. Decide whether it is even, odd, or neither.
-

Accepted Answer

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

Question 20

Determine whether the equation defines y as a function of x.
-$y^{2}+x=2$

Accepted Answer

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

Find and simplify the difference quotient of f, $\frac { f ( x + h ) - f ( x ) } { h }$ $\mathbf { h } \neq 0$ , for the function. - $f ( x ) = \frac { 1 } { 7 x }$

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 1 ; ( - 5,5 )$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( - 1,0 )$

The graph of a function f is given. Use the graph to answer the question. -How often does the line y = 20 intersect the graph?

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the x-axis

The graph of a function is given. Decide whether it is even, odd, or neither. -

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 2 x + 5 ; g ( x ) = 6 x - 1$ Find $\frac { f } { g }$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 16 - x ^ { 2 } ; g ( x ) = 4 - x$ Find $f + g$ .

Find the average rate of change for the function between the given values. - $f ( x ) = - 3 x ^ { 2 } - x$ ; from 5 to 6

Find the value for the function. -Find $f ( 2 x )$ when $f ( x ) = \sqrt { 2 x ^ { 2 } - 7 x }$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 7 x + 3 ; g ( x ) = 3 x + 7$ Find f $\cdot g .$

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. - $f ( x ) = x ^ { 5 } - x ^ { 2 } ; ( - 2,2 )$

The graph of a function is given. Decide whether it is even, odd, or neither. -

Determine whether the equation defines y as a function of x. - $y^{2}+x=2$

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

Find and simplify the difference quotient of f, f(x+h)−f(x)h\frac { f ( x + h ) - f ( x ) } { h }hf(x+h)−f(x)​ h≠0\mathbf { h } \neq 0h=0 , for the function. - f(x)=17xf ( x ) = \frac { 1 } { 7 x }f(x)=7x1​

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. - f(x)=x3−3x2+1;(−5,5)f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 1 ; ( - 5,5 )f(x)=x3−3x2+1;(−5,5)

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - (−1,0)( - 1,0 )(−1,0)

The graph of a function f is given. Use the graph to answer the question. -How often does the line y = 20 intersect the graph?

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)=−1xf ( x ) = - \frac { 1 } { x }f(x)=−x1​ A) B) C) D)

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the x-axis

The graph of a function is given. Decide whether it is even, odd, or neither. -

For the given functions f and g, find the requested function and state its domain. - f(x)=2x+5;g(x)=6x−1f ( x ) = 2 x + 5 ; g ( x ) = 6 x - 1f(x)=2x+5;g(x)=6x−1 Find fg\frac { f } { g }gf​ .

For the given functions f and g, find the requested function and state its domain. - f(x)=16−x2;g(x)=4−xf ( x ) = 16 - x ^ { 2 } ; g ( x ) = 4 - xf(x)=16−x2;g(x)=4−x Find f+gf + gf+g .

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+2)3f(x)=(x+2)^{3}f(x)=(x+2)3 A) B) C) D)

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+3)2−2f(x)=-(x+3)^{2}-2f(x)=−(x+3)2−2 A) B) C) D)

Find the average rate of change for the function between the given values. - f(x)=−3x2−xf ( x ) = - 3 x ^ { 2 } - xf(x)=−3x2−x ; from 5 to 6

Graph the function. - f(x)={x−1 if x<1−5 if x≥1f ( x ) = \left\{ \begin{array} { l l } x - 1 & \text { if } x < 1 \\- 5 & \text { if } x \geq 1\end{array} \right.f(x)={x−1−5​ if x<1 if x≥1​ A) B) C) D)

Find the value for the function. -Find f(2x)f ( 2 x )f(2x) when f(x)=2x2−7xf ( x ) = \sqrt { 2 x ^ { 2 } - 7 x }f(x)=2x2−7x​ .

For the given functions f and g, find the requested function and state its domain. - f(x)=7x+3;g(x)=3x+7f ( x ) = 7 x + 3 ; g ( x ) = 3 x + 7f(x)=7x+3;g(x)=3x+7 Find f ⋅g.\cdot g .⋅g.

The graph of a function is given. Decide whether it is even, odd, or neither. -

Determine whether the equation defines y as a function of x. - y2+x=2y^{2}+x=2y2+x=2

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

Find and simplify the difference quotient of f, $\frac { f ( x + h ) - f ( x ) } { h }$ $\mathbf { h } \neq 0$ , for the function. - $f ( x ) = \frac { 1 } { 7 x }$

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } + 1 ; ( - 5,5 )$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( - 1,0 )$

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 2 x + 5 ; g ( x ) = 6 x - 1$ Find $\frac { f } { g }$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 16 - x ^ { 2 } ; g ( x ) = 4 - x$ Find $f + g$ .

Find the average rate of change for the function between the given values. - $f ( x ) = - 3 x ^ { 2 } - x$ ; from 5 to 6

Find the value for the function. -Find $f ( 2 x )$ when $f ( x ) = \sqrt { 2 x ^ { 2 } - 7 x }$ .

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = 7 x + 3 ; g ( x ) = 3 x + 7$ Find f $\cdot g .$

Determine whether the equation defines y as a function of x. - $y^{2}+x=2$