Question 1

Find the difference quotient and simplify your answer.
$$f ( s ) = - 2 s ^ { 2 } - 2 s , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0$$

Accepted Answer

A)  $6 + h$ 
B)  $- 18 - 2 s - \frac { 16 } { s }$ 
C)  $- 2 - 2 s - \frac { 16 } { s }$ 
D)  $- 2 - 2 h$ 
E)  $- 18 - 2 h$ 
A)  $6 + h$ 
B)  $- 18 - 2 s - \frac { 16 } { s }$ 
C)  $- 2 - 2 s - \frac { 16 } { s }$ 
D)  $- 2 - 2 h$ 
E)  $- 18 - 2 h$

Question 2

The scatter plots of different data are shown below.Determine whether there is a positive correlation, negative correlation, or no discernible correlation between the
Variables.

Accepted Answer

A)  positive correlation 
B)  negative correlation 
C)  no discernible correlation 
A)  positive correlation 
B)  negative correlation 
C)  no discernible correlation

Question 3

Compare the graph of the following function with the graph of $f ( x ) = | x |$.
$$y = \left| \frac { 1 } { 9 } x \right|$$

Accepted Answer

A)  vertical shift of $\frac { 1 } { 9 }$ unit up 
B)  horizontal stretch of $\frac { 9 } { 1 }$ unit 
C)  vertical shrink of $\frac { 1 } { 9 }$ unit 
D)  horizontal shrink of $\frac { 1 } { 9 }$ unit vertical shift of $\frac { 9 } { 1 }$ unit 
E)  horizontal shrink of $\frac { 1 } { 9 }$ unit 
A)  vertical shift of $\frac { 1 } { 9 }$ unit up 
B)  horizontal stretch of $\frac { 9 } { 1 }$ unit 
C)  vertical shrink of $\frac { 1 } { 9 }$ unit 
D)  horizontal shrink of $\frac { 1 } { 9 }$ unit vertical shift of $\frac { 9 } { 1 }$ unit 
E)  horizontal shrink of $\frac { 1 } { 9 }$ unit

Question 4

Determine an equation that may represented by the graph shown below.

Accepted Answer

A)  $f ( x ) = - 1 + \sqrt { 1 + x }$ 
B)  $f ( x ) = 1 - \sqrt { 1 - x }$ 
C)  $f ( x ) = - 1 - \sqrt { 1 - x }$ 
D)  $f ( x ) = - 1 + \sqrt { 1 - x }$ 
E)  $f ( x ) = - 1 - \sqrt { 1 + x }$ 
A)  $f ( x ) = - 1 + \sqrt { 1 + x }$ 
B)  $f ( x ) = 1 - \sqrt { 1 - x }$ 
C)  $f ( x ) = - 1 - \sqrt { 1 - x }$ 
D)  $f ( x ) = - 1 + \sqrt { 1 - x }$ 
E)  $f ( x ) = - 1 - \sqrt { 1 + x }$

Question 5

Find the value(s) of $x$ for which $f ( x ) = g ( x )$.
$f ( x ) = x ^ { 2 } - 7 x + 3 \quad g ( x ) = - 3 x + 8$

Accepted Answer

A)  $3,10 , \frac { 8 } { 3 }$ 
B)  $3 , - 7 , \frac { 8 } { 3 }$ 
C)  $5 , - 1$ 
D)  $- 5,1$ 
E)  $4 , \frac { 8 } { 3 }$ 
A)  $3,10 , \frac { 8 } { 3 }$ 
B)  $3 , - 7 , \frac { 8 } { 3 }$ 
C)  $5 , - 1$ 
D)  $- 5,1$ 
E)  $4 , \frac { 8 } { 3 }$

Question 6

Find $f \circ g$.
$f ( x ) = \left| x ^ { 2 } - 6 \right|$
$g ( x ) = - 9 - x$

Accepted Answer

A)  $( f \circ g ) ( x ) = \left| x ^ { 2 } + 18 x + 75 \right|$ 
B)  $( f \circ g ) ( x ) = \left| x ^ { 2 } + 75 \right|$ 
C)  $( f \circ g ) ( x ) = \left| - 3 - x ^ { 2 } \right|$ 
D)  $( f \circ g ) ( x ) = \left| - 15 - x ^ { 2 } \right|$ 
E)  $( f \circ g ) ( x ) = - 9 - \left| x ^ { 2 } - 6 \right|$ 
A)  $( f \circ g ) ( x ) = \left| x ^ { 2 } + 18 x + 75 \right|$ 
B)  $( f \circ g ) ( x ) = \left| x ^ { 2 } + 75 \right|$ 
C)  $( f \circ g ) ( x ) = \left| - 3 - x ^ { 2 } \right|$ 
D)  $( f \circ g ) ( x ) = \left| - 15 - x ^ { 2 } \right|$ 
E)  $( f \circ g ) ( x ) = - 9 - \left| x ^ { 2 } - 6 \right|$

Question 7

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. $$f ( x ) = 2 x ^ { 4 } - 4 x ^ { 2 }$$

Accepted Answer

A) 
decreasing on $( 0,0 )$
increasing on $( 0 , \infty )$ 
B) 
increasing on $( - \infty , - 1 )$
decreasing on $( - 1,0 )$
increasing on $( 0,1 )$
decreasing on $( 1 , \infty )$ 
C) 
decreasing on $( - \infty , - 1 )$
increasing on $( - 1,1 )$
decreasing on $( 1 , \infty )$ 
D) 
increasing on $( - \infty , 0 )$
decreasing on $( 0 , \infty )$ 
E) 
decreasing on $( - \infty , - 1 )$
increasing on $( - 1,0 )$
decreasing on $( 0,1 )$
increasing on $( 1 , \infty )$ 
A) 
decreasing on $( 0,0 )$
increasing on $( 0 , \infty )$ 
B) 
increasing on $( - \infty , - 1 )$
decreasing on $( - 1,0 )$
increasing on $( 0,1 )$
decreasing on $( 1 , \infty )$ 
C) 
decreasing on $( - \infty , - 1 )$
increasing on $( - 1,1 )$
decreasing on $( 1 , \infty )$ 
D) 
increasing on $( - \infty , 0 )$
decreasing on $( 0 , \infty )$ 
E) 
decreasing on $( - \infty , - 1 )$
increasing on $( - 1,0 )$
decreasing on $( 0,1 )$
increasing on $( 1 , \infty )$

Question 8

Find the inverse function of $f ( x ) = 8 x + 3$

Accepted Answer

A)  $g ( x ) = \frac { x - 3 } { 8 }$ 
B)  $g ( x ) = 3 x + 8$ 
C)  $\quad g ( x ) = \frac { x + 3 } { 8 }$ 
D)  $\quad g ( x ) = \frac { x } { 3 }$ 
E)  $\quad g ( x ) = \frac { 1 } { 8 } x - 3$ 
A)  $g ( x ) = \frac { x - 3 } { 8 }$ 
B)  $g ( x ) = 3 x + 8$ 
C)  $\quad g ( x ) = \frac { x + 3 } { 8 }$ 
D)  $\quad g ( x ) = \frac { x } { 3 }$ 
E)  $\quad g ( x ) = \frac { 1 } { 8 } x - 3$

Question 9

Use the graphs of $f$ and $g$, shown below, to graph $h ( x ) = ( f + g ) ( x )$.

Accepted Answer

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

Question 10

Evaluate the function at the specified value of the independent variable and simplify. $$f ( y ) = 2 y + 7$$
$f ( - 1.4 )$

Accepted Answer

A)  $- 2.8 \mathrm { y } + 14$ 
B)  $- 9.8$ 
C)  $4.2$ 
D)  $- 1.4 y + 7$ 
E)  $- 1.4 y - 7$ 
A)  $- 2.8 \mathrm { y } + 14$ 
B)  $- 9.8$ 
C)  $4.2$ 
D)  $- 1.4 y + 7$ 
E)  $- 1.4 y - 7$

Question 11

Use the graph of the function to find the domain and range of $f$.

Accepted Answer

A) 
domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range : $( - \infty , - 2 ) \cup ( - 1 , \infty )$ 
B) 
domain : $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range : $\{ - 2 , - 1 \}$ 
C) 
domain : all real numbers
range: $\{ - 2 , - 1 \}$ 
D) 
domain : $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range : $( - 1,1 )$ 
E) 
domain : $\{ - 2 , - 1 \}$
range: all real numbers 
A) 
domain: $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range : $( - \infty , - 2 ) \cup ( - 1 , \infty )$ 
B) 
domain : $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range : $\{ - 2 , - 1 \}$ 
C) 
domain : all real numbers
range: $\{ - 2 , - 1 \}$ 
D) 
domain : $( - \infty , - 2 ) \cup ( - 2 , \infty )$
range : $( - 1,1 )$ 
E) 
domain : $\{ - 2 , - 1 \}$
range: all real numbers

Question 12

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = - f ( x - 2 )$

Accepted Answer

A)  even 
B)  odd 
C)  cannot be determined 
D)  neither 
A)  even 
B)  odd 
C)  cannot be determined 
D)  neither

Question 13

Find all real values of $x$ such that $f ( x ) = 0$.
$$f ( x ) = \frac { 7 x - 5 } { 7 }$$

Accepted Answer

A)  $\frac { 5 } { 49 }$ 
B)  $\pm \frac { 5 } { 49 }$ 
C)  $\pm \frac { 5 } { 7 }$ 
D)  $\frac { 5 } { 7 }$ 
E)  $- \frac { 5 } { 7 }$ 
A)  $\frac { 5 } { 49 }$ 
B)  $\pm \frac { 5 } { 49 }$ 
C)  $\pm \frac { 5 } { 7 }$ 
D)  $\frac { 5 } { 7 }$ 
E)  $- \frac { 5 } { 7 }$

Question 14

Plot the points and find the slope of the line passing through the pair of points. $( 3,4 ) , ( - 2,4 )$

Accepted Answer

A)  slope: 0 
B)  slope: 1 
C)  slope: $- 5$ 
D)  slope: $- \frac { 1 } { 5 }$ 
E)  slope: undefined 
A)  slope: 0 
B)  slope: 1 
C)  slope: $- 5$ 
D)  slope: $- \frac { 1 } { 5 }$ 
E)  slope: undefined

Question 15

Plot the points and find the slope of the line passing through the pair of points. $( 1,0 ) , ( 5,3 )$

Accepted Answer

A)  slope: $\frac { 4 } { 3 }$ 
B)  slope: $- \frac { 4 } { 3 }$ 
C)  slope: $\frac { 1 } { 2 }$ 
D)  slope: $\frac { 3 } { 4 }$ 
E)  slope: $- \frac { 3 } { 4 }$ 
A)  slope: $\frac { 4 } { 3 }$ 
B)  slope: $- \frac { 4 } { 3 }$ 
C)  slope: $\frac { 1 } { 2 }$ 
D)  slope: $\frac { 3 } { 4 }$ 
E)  slope: $- \frac { 3 } { 4 }$

Question 16

Find the slope and y-intercept of the equation of the line. $$y = - 2 x - 9$$

Accepted Answer

A)  slope: $- \frac { 1 } { 2 } ; y$-intercept: $- 9$ 
B)  slope: $- \frac { 1 } { 9 } ; y$-intercept: $- 2$ 
C)  slope: $- 2 ; y$-intercept: $- 9$ 
D)  slope: $- 9 ; y$-intercept: $- 2$ 
E)  slope: $- 2 ; y$-intercept: 9 
A)  slope: $- \frac { 1 } { 2 } ; y$-intercept: $- 9$ 
B)  slope: $- \frac { 1 } { 9 } ; y$-intercept: $- 2$ 
C)  slope: $- 2 ; y$-intercept: $- 9$ 
D)  slope: $- 9 ; y$-intercept: $- 2$ 
E)  slope: $- 2 ; y$-intercept: 9

Question 17

Find $( f + g ) ( x )$
$$\begin{array} { l } 
f ( x ) = - 8 x ^ { 2 } + 5 x - 2 \
g ( x ) = 4 x ^ { 2 } + 7 x + 4
\end{array}$$

Accepted Answer

A)  $( f + g ) ( x ) = - 12 x ^ { 4 } - 2 x ^ { 2 } - 6$ 
B)  $( f + g ) ( x ) = - 4 x ^ { 4 } + 12 x ^ { 2 } + 2$ 
C)  $( f + g ) ( x ) = - 12 x ^ { 2 } - 2 x - 6$ 
D)  $( f + g ) ( x ) = - 4 x ^ { 2 } + 12 x + 2$ 
E)  $( f + g ) ( x ) = 4 x ^ { 2 } - 12 x - 2$ 
A)  $( f + g ) ( x ) = - 12 x ^ { 4 } - 2 x ^ { 2 } - 6$ 
B)  $( f + g ) ( x ) = - 4 x ^ { 4 } + 12 x ^ { 2 } + 2$ 
C)  $( f + g ) ( x ) = - 12 x ^ { 2 } - 2 x - 6$ 
D)  $( f + g ) ( x ) = - 4 x ^ { 2 } + 12 x + 2$ 
E)  $( f + g ) ( x ) = 4 x ^ { 2 } - 12 x - 2$

Question 18

Compare the graph of the following function with the graph of $f ( x ) = | x |$.
$$y = \left| \frac { 3 } { 4 } x \right|$$

Accepted Answer

A)  vertical shift of $\frac { 3 } { 4 }$ units up 
B)  horizontal stretch of $\frac { 4 } { 3 }$ units 
C)  vertical shrink of $\frac { 3 } { 4 }$ units 
D)  horizontal shrink of $\frac { 3 } { 4 }$ units vertical shift of $\frac { 4 } { 3 }$ units 
E)  horizontal shrink of $\frac { 3 } { 4 }$ units 
A)  vertical shift of $\frac { 3 } { 4 }$ units up 
B)  horizontal stretch of $\frac { 4 } { 3 }$ units 
C)  vertical shrink of $\frac { 3 } { 4 }$ units 
D)  horizontal shrink of $\frac { 3 } { 4 }$ units vertical shift of $\frac { 4 } { 3 }$ units 
E)  horizontal shrink of $\frac { 3 } { 4 }$ units

Question 19

Graph the function and determine the interval(s) for which $f ( x ) \geq 0$.
$$f ( x ) = - x ^ { 2 } + 4 x$$

Accepted Answer

A)  $( - \infty , 0 ] \cup [ 4 , \infty )$ 
B)  $[ 0,4 ]$ 
C)  $( 0,4 )$ 
D)  $( - \infty , 0 ) \cup ( 4 , \infty )$ 
E)  $\{ 4 \}$ 
A)  $( - \infty , 0 ] \cup [ 4 , \infty )$ 
B)  $[ 0,4 ]$ 
C)  $( 0,4 )$ 
D)  $( - \infty , 0 ) \cup ( 4 , \infty )$ 
E)  $\{ 4 \}$

Find the difference quotient and simplify your answer. $f ( s ) = - 2 s ^ { 2 } - 2 s , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0$

The scatter plots of different data are shown below.Determine whether there is a positive correlation, negative correlation, or no discernible correlation between the Variables.

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 1 } { 9 } x \right|$

Determine an equation that may represented by the graph shown below.

Find the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 7 x + 3 \quad g ( x ) = - 3 x + 8$

Find $f \circ g$ . $f ( x ) = \left| x ^ { 2 } - 6 \right|$ $g ( x ) = - 9 - x$

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. $f ( x ) = 2 x ^ { 4 } - 4 x ^ { 2 }$

Find the inverse function of $f ( x ) = 8 x + 3$

Use the graphs of $f$ and $g$ , shown below, to graph $h ( x ) = ( f + g ) ( x )$ .

Evaluate the function at the specified value of the independent variable and simplify. $f ( y ) = 2 y + 7$ $f ( - 1.4 )$

Use the graph of the function to find the domain and range of $f$ .

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = - f ( x - 2 )$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = \frac { 7 x - 5 } { 7 }$

Plot the points and find the slope of the line passing through the pair of points. $( 3,4 ) , ( - 2,4 )$

Plot the points and find the slope of the line passing through the pair of points. $( 1,0 ) , ( 5,3 )$

Find the slope and y-intercept of the equation of the line. $y = - 2 x - 9$

Find $( f + g ) ( x )$ f(x)=-8+5x-2 g(x)=4+7x+4

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 3 } { 4 } x \right|$

Graph the function and determine the interval(s) for which $f ( x ) \geq 0$ . $f ( x ) = - x ^ { 2 } + 4 x$ $Graph the function and determine the interval(s) for which f ( x ) \geq 0 . f ( x ) = - x ^ { 2 } + 4 x$

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Calculus Practice Problems

Filters

Exam 1: Functions and Their Graphs

Find the difference quotient and simplify your answer. f(s)=−2s2−2s,f(4+h)−f(4)h,h≠0f ( s ) = - 2 s ^ { 2 } - 2 s , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0f(s)=−2s2−2s,hf(4+h)−f(4)​,h=0

The scatter plots of different data are shown below.Determine whether there is a positive correlation, negative correlation, or no discernible correlation between the Variables.

Compare the graph of the following function with the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ . y=∣19x∣y = \left| \frac { 1 } { 9 } x \right|y=​91​x​

Determine an equation that may represented by the graph shown below.

Find the value(s) of xxx for which f(x)=g(x)f ( x ) = g ( x )f(x)=g(x) . f(x)=x2−7x+3g(x)=−3x+8f ( x ) = x ^ { 2 } - 7 x + 3 \quad g ( x ) = - 3 x + 8f(x)=x2−7x+3g(x)=−3x+8

Find f∘gf \circ gf∘g . f(x)=∣x2−6∣f ( x ) = \left| x ^ { 2 } - 6 \right|f(x)=​x2−6​ g(x)=−9−xg ( x ) = - 9 - xg(x)=−9−x

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. f(x)=2x4−4x2f ( x ) = 2 x ^ { 4 } - 4 x ^ { 2 }f(x)=2x4−4x2

Find the inverse function of f(x)=8x+3f ( x ) = 8 x + 3f(x)=8x+3

Use the graphs of fff and ggg , shown below, to graph h(x)=(f+g)(x)h ( x ) = ( f + g ) ( x )h(x)=(f+g)(x) .

Evaluate the function at the specified value of the independent variable and simplify. f(y)=2y+7f ( y ) = 2 y + 7f(y)=2y+7 f(−1.4)f ( - 1.4 )f(−1.4)

Use the graph of the function to find the domain and range of fff .

If fff is an even function, determine if ggg is even, odd, or neither. g(x)=−f(x−2)g ( x ) = - f ( x - 2 )g(x)=−f(x−2)

Find all real values of xxx such that f(x)=0f ( x ) = 0f(x)=0 . f(x)=7x−57f ( x ) = \frac { 7 x - 5 } { 7 }f(x)=77x−5​

Plot the points and find the slope of the line passing through the pair of points. (3,4),(−2,4)( 3,4 ) , ( - 2,4 )(3,4),(−2,4)

Plot the points and find the slope of the line passing through the pair of points. (1,0),(5,3)( 1,0 ) , ( 5,3 )(1,0),(5,3)

Find the slope and y-intercept of the equation of the line. y=−2x−9y = - 2 x - 9y=−2x−9

Find (f+g)(x)( f + g ) ( x )(f+g)(x) f(x)=-8+5x-2 g(x)=4+7x+4

Compare the graph of the following function with the graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ . y=∣34x∣y = \left| \frac { 3 } { 4 } x \right|y=​43​x​

Graph the function and determine the interval(s) for which f(x)≥0f ( x ) \geq 0f(x)≥0 . f(x)=−x2+4xf ( x ) = - x ^ { 2 } + 4 xf(x)=−x2+4x

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Linear Systems and Matrices

Sequences, Series, and Probability

Topics in Analytic Geometry

Analytic Geometry in Three Dimensions

Calculus Practice Problems

Filters

Find the difference quotient and simplify your answer. $f ( s ) = - 2 s ^ { 2 } - 2 s , \quad \frac { f ( 4 + h ) - f ( 4 ) } { h } , h \neq 0$

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 1 } { 9 } x \right|$

Find the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 7 x + 3 \quad g ( x ) = - 3 x + 8$

Find $f \circ g$ . $f ( x ) = \left| x ^ { 2 } - 6 \right|$ $g ( x ) = - 9 - x$

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. $f ( x ) = 2 x ^ { 4 } - 4 x ^ { 2 }$

Find the inverse function of $f ( x ) = 8 x + 3$

Use the graphs of $f$ and $g$ , shown below, to graph $h ( x ) = ( f + g ) ( x )$ .

Evaluate the function at the specified value of the independent variable and simplify. $f ( y ) = 2 y + 7$ $f ( - 1.4 )$

Use the graph of the function to find the domain and range of $f$ .

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = - f ( x - 2 )$

Find all real values of $x$ such that $f ( x ) = 0$ . $f ( x ) = \frac { 7 x - 5 } { 7 }$

Plot the points and find the slope of the line passing through the pair of points. $( 3,4 ) , ( - 2,4 )$

Plot the points and find the slope of the line passing through the pair of points. $( 1,0 ) , ( 5,3 )$

Find the slope and y-intercept of the equation of the line. $y = - 2 x - 9$

Find $( f + g ) ( x )$ f(x)=-8+5x-2 g(x)=4+7x+4

Compare the graph of the following function with the graph of $f ( x ) = | x |$ . $y = \left| \frac { 3 } { 4 } x \right|$

Graph the function and determine the interval(s) for which $f ( x ) \geq 0$ . $f ( x ) = - x ^ { 2 } + 4 x$ $Graph the function and determine the interval(s) for which f ( x ) \geq 0 . f ( x ) = - x ^ { 2 } + 4 x$