Question 1

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-$$( - 4,1 )$$

Accepted Answer

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

Question 2

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 maximum. What are the local maxima?   A) $f$ has a local maximum at $x = - \pi$ and $\pi$; the local maximum is 2

Accepted Answer

B)  f has no local maximum 
C)  $\mathrm { f }$ has a local maximum at $x = 0$; the local maximum is $- 2$ 
D)  $\mathrm { f }$ has a local maximum at $- \pi$; the local maximum is 2 
B)  f has no local maximum 
C)  $\mathrm { f }$ has a local maximum at $x = 0$; the local maximum is $- 2$ 
D)  $\mathrm { f }$ has a local maximum at $- \pi$; the local maximum is 2 A

Question 3

Find the value for the function.
-$\text { Find } f(-9) \text { when } f(x)=|x|-6$

Accepted Answer

A)  15 
B) -15 
C)  -3 
D) 3 
A)  15 
B) -15 
C)  -3 
D) 3 D

Question 4

The graph of a piecewise-defined function is given. Write a definition for the function.
-  A)
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x + \frac { 1 } { 2 } & \text { if } 3 < x \leq 5 \end{array} \right.$

Accepted Answer

B) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x - \frac { 1 } { 2 } & \text { if } 3 < x \leq 5 \end{array} \right.$ 
C) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x & \text { if } 3 < x \leq 5 \end{array} \right.$ 
D) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x + 2 & \text { if } 3 < x \leq 5 \end{array} \right.$ 
B) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x - \frac { 1 } { 2 } & \text { if } 3 < x \leq 5 \end{array} \right.$ 
C) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x & \text { if } 3 < x \leq 5 \end{array} \right.$ 
D) 
$f ( x ) = \left\{ \begin{array} { l l } x + 1 & \text { if } 0 \leq x \leq 3 \ \frac { 1 } { 2 } x + 2 & \text { if } 3 < x \leq 5 \end{array} \right.$

Question 5

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

Accepted Answer

B)  $y = \sqrt { x }$ 
C)  $y = \sqrt { x + 1 }$ 
D)  $y = \sqrt { x - 1 }$ 
B)  $y = \sqrt { x }$ 
C)  $y = \sqrt { x + 1 }$ 
D)  $y = \sqrt { x - 1 }$

Question 6

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-$$( - 2 , - 1 )$$

Accepted Answer

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

Question 7

Find the domain of the function.
-$$f ( x ) = \sqrt { 24 - x }$$

Accepted Answer

A)  $\{ x \mid x \neq 24 \}$ 
B)  $\{ x \mid x \leq 2 \sqrt { 6 } \}$ 
C)  $\{ x \mid x \neq 2 \sqrt { 6 } \}$ 
D)  $\{ x \mid x \leq 24 \}$ 
A)  $\{ x \mid x \neq 24 \}$ 
B)  $\{ x \mid x \leq 2 \sqrt { 6 } \}$ 
C)  $\{ x \mid x \neq 2 \sqrt { 6 } \}$ 
D)  $\{ x \mid x \leq 24 \}$

Question 8

Determine whether the relation represents a function. If it is a function, state the domain and range.
-$\left\{(2.44,3.24),(2.444,-3.2),\left(\frac{7}{3}, 0\right),(2.33,-2)\right\}$

Accepted Answer

A)  function
domain: $ \{3.24,-3.2,0,-2\} $
range: $ \left\{2.44,2.444, \frac{7}{3}, 2.33\right\} $ 
B)  function
domain: $ \left\{2.44,2.444, \frac{7}{3}, 2.33\right\} $
range: $ \{3.24,-3.2,0,-2\} $ 
C)  $\text { not a function }$ 
A)  function
domain: $ \{3.24,-3.2,0,-2\} $
range: $ \left\{2.44,2.444, \frac{7}{3}, 2.33\right\} $ 
B)  function
domain: $ \left\{2.44,2.444, \frac{7}{3}, 2.33\right\} $
range: $ \{3.24,-3.2,0,-2\} $ 
C)  $\text { not a function }$

Question 9

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

A)

Accepted Answer

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

Question 10

Find and simplify the difference quotient of f, $$\frac { f ( x + h ) - f ( x ) } { h }$$ $\mathbf { h } \neq 0$ , for the function.
-  A)
function
domain: all real numbers
range: $ \{y \mid y \leq-2 $ or $ y \geq 2\} $
intercepts: $ (-2,0),(2,0) $
symmetry: $ y $-axis\[\begin{array} { l l }

Accepted Answer

B) 
function
domain: $ \{x \mid-2 \leq x \leq 2\} $
range: all real numbers
intercepts: $ (-2,0),(2,0) $
symmetry: $ \mathrm{x} $-axis, $ y $-axis 
C) 
function
domain: $ \{x \mid x \leq-2 $ or $ x \geq 2\} $
range: all real numbers
intercepts: $ (-2,0),(2,0) $
symmetry: $ \mathrm{x} $-axis, $ \mathrm{y} $-axis, origirn 
D) 
$\text { not a function }$ 
B) 
function
domain: $ \{x \mid-2 \leq x \leq 2\} $
range: all real numbers
intercepts: $ (-2,0),(2,0) $
symmetry: $ \mathrm{x} $-axis, $ y $-axis 
C) 
function
domain: $ \{x \mid x \leq-2 $ or $ x \geq 2\} $
range: all real numbers
intercepts: $ (-2,0),(2,0) $
symmetry: $ \mathrm{x} $-axis, $ \mathrm{y} $-axis, origirn 
D) 
$\text { not a function }$

Question 11

Graph the function by starting with the graph of the basic function and then using the techniques of shifting,
compressing, stretching, and/or reflecting.
-$f(x)=7 x^{2}$
 
 A)

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

The graph of a function f is given. Use the graph to answer the question.
-Is f(3) positive or negative?

Accepted Answer

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

Question 14

For the function, find the average rate of change of f from 1 to x: $$\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$$
-$$f ( x ) = x ^ { 2 } - 2 x$$

Accepted Answer

A)  1 
B)  $\frac { x ^ { 2 } - 2 x - 1 } { x - 1 }$ 
C)  $x - 1$ 
D)  $x + 1$ 
A)  1 
B)  $\frac { x ^ { 2 } - 2 x - 1 } { x - 1 }$ 
C)  $x - 1$ 
D)  $x + 1$

Question 15

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given
interval.
-$$( 0,3 )$$

Accepted Answer

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

Question 16

The graph of a piecewise-defined function is given. Write a definition for the function.
-  A)
$f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x - 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } 0 \leq x \leq 3 \end{array} \right.$

Accepted Answer

B) 
$f ( x ) = \left\{ \begin{array} { l l } \frac {3 } { 4} x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } 0 < x \leq 3 \end{array} \right.$ 
C) 
$f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x+ 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x+2 & \text { if } 0< x \leq 3 \end{array} \right.$ 
D) 
 $f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } 0< x \leq 3 \end{array} \right.$ 
B) 
$f ( x ) = \left\{ \begin{array} { l l } \frac {3 } { 4} x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } 0 < x \leq 3 \end{array} \right.$ 
C) 
$f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x+ 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x+2 & \text { if } 0< x \leq 3 \end{array} \right.$ 
D) 
 $f ( x ) = \left\{ \begin{array} { l l } \frac { 4 } { 3 } x + 4 & \text { if } - 3 \leq x \leq 0 \ \frac { 2 } { 3 } x & \text { if } 0< x \leq 3 \end{array} \right.$

Question 17

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.
-$$f ( x ) = \frac { 1 } { x - 6 } + 6$$
 
 A)

Accepted Answer

B)

C) 
  
D) 
  
B)

C) 
  
D)

Question 18

The graph of a function f is given. Use the graph to answer the question.
-What are the x-intercepts?

Accepted Answer

A)  $- 10 , - 6,7,10$ 
B)  $- 6,7$ 
C)  $- 6,7,10$ 
D)  $- 6$ 
A)  $- 10 , - 6,7,10$ 
B)  $- 6,7$ 
C)  $- 6,7,10$ 
D)  $- 6$

Question 19

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)  $( - \infty , - 6 )$
В) $[ - 10 , - 6 ) , ( 7,10 )$ 
C)  $( - 6 , \infty )$ 
D)  $( - 6,7 )$ 
A)  $( - \infty , - 6 )$
В) $[ - 10 , - 6 ) , ( 7,10 )$ 
C)  $( - 6 , \infty )$ 
D)  $( - 6,7 )$

Question 20

Solve the problem.
-Express the gross salary G of a person who earns $35 per hour as a function of the number x of hours worked. A) $G ( x ) = 35 x ^ { 2 }$

Accepted Answer

B)  $G ( x ) = \frac { 35 } { x }$ 
C)  $G ( x ) = 35 x$ 
D)  $\mathrm { G } ( \mathrm { x } ) = 35 + \mathrm { x }$ 
B)  $G ( x ) = \frac { 35 } { x }$ 
C)  $G ( x ) = 35 x$ 
D)  $\mathrm { G } ( \mathrm { x } ) = 35 + \mathrm { x }$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( - 4,1 )$

Find the value for the function. - $\text { Find } f(-9) \text { when } f(x)=|x|-6$

Match the correct function to the graph. - $Match the correct function to the graph. - A) y = x - 1 B) y = \sqrt { x } C) y = \sqrt { x + 1 } D) y = \sqrt { x - 1 }$ A) $y = x - 1$ B) $y = \sqrt { x }$ C) $y = \sqrt { x + 1 }$ D) $y = \sqrt { x - 1 }$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( - 2 , - 1 )$

Find the domain of the function. - $f ( x ) = \sqrt { 24 - x }$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\left\{(2.44,3.24),(2.444,-3.2),\left(\frac{7}{3}, 0\right),(2.33,-2)\right\}$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=|-x|$ A) B) C) D)

The graph of a function f is given. Use the graph to answer the question. -Is f(3) positive or negative?

For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = x ^ { 2 } - 2 x$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( 0,3 )$

The graph of a function f is given. Use the graph to answer the question. -What are the x-intercepts?

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

Solve the problem. -Express the gross salary G of a person who earns $35 per hour as a function of the number x of hours worked. A) $G ( x ) = 35 x ^ { 2 }$ B) $G ( x ) = \frac { 35 } { x }$ C) $G ( x ) = 35 x$ D) $\mathrm { G } ( \mathrm { x } ) = 35 + \mathrm { x }$

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 is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - (−4,1)( - 4,1 )(−4,1)

Find the value for the function. - Find f(−9) when f(x)=∣x∣−6\text { Find } f(-9) \text { when } f(x)=|x|-6 Find f(−9) when f(x)=∣x∣−6

Match the correct function to the graph. - A) y=x−1y = x - 1y=x−1 B) y=xy = \sqrt { x }y=x​ C) y=x+1y = \sqrt { x + 1 }y=x+1​ D) y=x−1y = \sqrt { x - 1 }y=x−1​

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - (−2,−1)( - 2 , - 1 )(−2,−1)

Find the domain of the function. - f(x)=24−xf ( x ) = \sqrt { 24 - x }f(x)=24−x​

Determine whether the relation represents a function. If it is a function, state the domain and range. - {(2.44,3.24),(2.444,−3.2),(73,0),(2.33,−2)}\left\{(2.44,3.24),(2.444,-3.2),\left(\frac{7}{3}, 0\right),(2.33,-2)\right\}{(2.44,3.24),(2.444,−3.2),(37​,0),(2.33,−2)}

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∣f(x)=|-x|f(x)=∣−x∣ 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)=7x2f(x)=7 x^{2}f(x)=7x2 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)2f(x)=(-x)^{2}f(x)=(−x)2 A) B) C) D)

The graph of a function f is given. Use the graph to answer the question. -Is f(3) positive or negative?

For the function, find the average rate of change of f from 1 to x: f(x)−f(1)x−1,x≠1\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1x−1f(x)−f(1)​,x=1 - f(x)=x2−2xf ( x ) = x ^ { 2 } - 2 xf(x)=x2−2x

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - (0,3)( 0,3 )(0,3)

The graph of a function f is given. Use the graph to answer the question. -What are the x-intercepts?

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

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

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( - 4,1 )$

Find the value for the function. - $\text { Find } f(-9) \text { when } f(x)=|x|-6$

Match the correct function to the graph. - $Match the correct function to the graph. - A) y = x - 1 B) y = \sqrt { x } C) y = \sqrt { x + 1 } D) y = \sqrt { x - 1 }$ A) $y = x - 1$ B) $y = \sqrt { x }$ C) $y = \sqrt { x + 1 }$ D) $y = \sqrt { x - 1 }$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( - 2 , - 1 )$

Find the domain of the function. - $f ( x ) = \sqrt { 24 - x }$

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\left\{(2.44,3.24),(2.444,-3.2),\left(\frac{7}{3}, 0\right),(2.33,-2)\right\}$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=|-x|$ A) B) C) D)

For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = x ^ { 2 } - 2 x$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( 0,3 )$

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