Question 1

Estimate the slope of the line.

Accepted Answer

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

Question 2

Find $( f + g ) ( x )$.
$f ( x ) = - 8 x ^ { 2 } + 5 x - 2$
$g ( x ) = 4 x ^ { 2 } + 7 x + 4$

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 3

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)  $\{ 4 \}$

Question 4

Determine whether the function is even, odd, or neither.
$f ( x ) = 4 x ^ { 3 } - 2 x$

Accepted Answer

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

Question 5

Given that $f ( x ) = \sqrt [ 4 ] { x - 4 }$ and $g ( x ) = x ^ { 4 } + 4$ determine the value of the following (if possible).
$( f \circ g ) ( 0 )$

Accepted Answer

A)  0 
B)  2 
C)  4 
D)  $x ^ { 4 } - 16$ 
E)  not possible 
A)  0 
B)  2 
C)  4 
D)  $x ^ { 4 } - 16$ 
E)  not possible

Question 6

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 1$ and $g ( x ) = x - 6$. $( f g ) ( - 2 )$

Accepted Answer

A)  $- 24$ 
B)  40 
C)  $- 2$ 
D)  12 
E)  24 
A)  $- 24$ 
B)  40 
C)  $- 2$ 
D)  12 
E)  24

Question 7

Find the slope and $y$-intercept of the equation of the line.
$y = - 2 x + 3$

Accepted Answer

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

Question 8

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 9

Evaluate the following function at the specified value of the independent variable and simplify.
$f ( u ) = \frac { 4 u ^ { 2 } + 12 } { u ^ { 2 } } ; \quad f ( 0 )$

Accepted Answer

A)  12 
B)  0 
C)  4 
D)  16 
E)  undefined 
A)  12 
B)  0 
C)  4 
D)  16 
E)  undefined

Question 10

Find $f \circ g$.
$f ( x ) = - 4 x + 3$

Accepted Answer

A)  $( f \circ g ) ( x ) = - 4 x - 25$
$g ( x ) = x + 7$ 
B)  $( f \circ g ) ( x ) = - 4 x + 10$ 
C)  $( f \circ g ) ( x ) = - 4 x ^ { 2 } - 25 x + 21$ 
D)  $( f \circ g ) ( x ) = - 5 x - 4$ 
E)  $\quad ( f \circ g ) ( x ) = - 5 x + 10$ 
A)  $( f \circ g ) ( x ) = - 4 x - 25$
$g ( x ) = x + 7$ 
B)  $( f \circ g ) ( x ) = - 4 x + 10$ 
C)  $( f \circ g ) ( x ) = - 4 x ^ { 2 } - 25 x + 21$ 
D)  $( f \circ g ) ( x ) = - 5 x - 4$ 
E)  $\quad ( f \circ g ) ( x ) = - 5 x + 10$

Question 11

Use the graph of $f$ to sketch the graph of the function indicated below.

Accepted Answer

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

Question 12

Evaluate the following function for $f ( x ) = - 2 x ^ { 2 } + 1$ and $g ( x ) = x + 4$ algebraically.
$\left( \frac { f } { g } \right) ( q - 4 )$

Accepted Answer

A)  $\frac { - 2 q ^ { 2 } + 5 } { q + 8 }$ 
B)  $\frac { - 2 q ^ { 2 } + 8 q - 31 } { q }$ 
C)  $\frac { - 2 q ^ { 2 } + 5 } { q }$ 
D)  $\frac { - 2 q ^ { 2 } + 16 q - 31 } { q }$ 
E)  $\frac { - 2 q ^ { 2 } - 3 } { q }$ 
A)  $\frac { - 2 q ^ { 2 } + 5 } { q + 8 }$ 
B)  $\frac { - 2 q ^ { 2 } + 8 q - 31 } { q }$ 
C)  $\frac { - 2 q ^ { 2 } + 5 } { q }$ 
D)  $\frac { - 2 q ^ { 2 } + 16 q - 31 } { q }$ 
E)  $\frac { - 2 q ^ { 2 } - 3 } { q }$

Question 13

Find $( f - g ) ( x )$.
$f ( x ) = - \frac { 8 x } { 4 x + 7 } \quad g ( x ) = - \frac { 4 } { x }$

Accepted Answer

A)  $( f - g ) ( x ) = \frac { - 8 x + 4 } { 3 x + 7 }$ 
B)  $( f - g ) ( x ) = \frac { - 8 x + 23 } { 4 x + 7 }$ 
C)  $( f - g ) ( x ) = \frac { - 8 x + 9 } { 4 x + 7 }$ 
D)  $( f - g ) ( x ) = \frac { - 8 x ^ { 2 } + 16 x - 28 } { 4 x ^ { 2 } + 7 x }$ 
E)  $( f - g ) ( x ) = \frac { - 8 x ^ { 2 } + 16 x + 28 } { 4 x ^ { 2 } + 7 x }$ 
A)  $( f - g ) ( x ) = \frac { - 8 x + 4 } { 3 x + 7 }$ 
B)  $( f - g ) ( x ) = \frac { - 8 x + 23 } { 4 x + 7 }$ 
C)  $( f - g ) ( x ) = \frac { - 8 x + 9 } { 4 x + 7 }$ 
D)  $( f - g ) ( x ) = \frac { - 8 x ^ { 2 } + 16 x - 28 } { 4 x ^ { 2 } + 7 x }$ 
E)  $( f - g ) ( x ) = \frac { - 8 x ^ { 2 } + 16 x + 28 } { 4 x ^ { 2 } + 7 x }$

Question 14

Match the graph of the function shown below with the graph of its inverse function

Accepted Answer

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

Question 15

Use the graphs of $y = f ( x )$ and $y = g ( x )$ to evaluate $\left( g ^ { - 1 } \circ f ^ { - 1 } \right) ( - 4 )$

Accepted Answer

A)  4 
B)  $1.3$ 
C)  0 
D)  $- 2$ 
E)  $- 2.5$ 
A)  4 
B)  $1.3$ 
C)  0 
D)  $- 2$ 
E)  $- 2.5$

Question 16

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line.
point: $( - 4,7 )$
line: $- 5 x - 15 y = - 6$

Accepted Answer

A)  $y = \frac { 1 } { 5 } x + \frac { 39 } { 5 }$ 
B)  $y = - \frac { 1 } { 3 } x + \frac { 17 } { 3 }$ 
C)  $y = 3 x + 19$ 
D)  $y = - 5 x + 27$ 
E)  $y = 3 x - \frac { 5 } { 3 }$ 
A)  $y = \frac { 1 } { 5 } x + \frac { 39 } { 5 }$ 
B)  $y = - \frac { 1 } { 3 } x + \frac { 17 } { 3 }$ 
C)  $y = 3 x + 19$ 
D)  $y = - 5 x + 27$ 
E)  $y = 3 x - \frac { 5 } { 3 }$

Question 17

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 49 }$.

Accepted Answer

A)  $[ - 7,7 ]$ 
B)  $( - 7,0 ] \cup [ 0,7 )$ 
C)  $( - \infty , - 7 ) \cup ( - 7,7 ) \cup ( 7 , \infty )$ 
D)  $( - \infty , - 7 ] \cup [ 7 , \infty )$ 
E)  $( - \infty , \infty )$ 
A)  $[ - 7,7 ]$ 
B)  $( - 7,0 ] \cup [ 0,7 )$ 
C)  $( - \infty , - 7 ) \cup ( - 7,7 ) \cup ( 7 , \infty )$ 
D)  $( - \infty , - 7 ] \cup [ 7 , \infty )$ 
E)  $( - \infty , \infty )$

Question 18

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( x + 4 )$

Accepted Answer

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

Question 19

Evaluate the function at the specified value of the independent variable and simplify.
$\begin{array} { l } 
f ( p ) = \frac { - 3 p } { 4 p - 3 } \
f ( s + 8 )
\end{array}$

Accepted Answer

A)  $\frac { - 3 s - 24 } { 4 s + 29 }$ 
B)  $\frac { - 3 s + 24 } { 4 s + 29 }$ 
C)  $\frac { - 3 p - 24 } { 4 p + 29 }$ 
D)  $\frac { 24 } { 35 }$ 
E)  $- \frac { 24 } { 29 }$ 
A)  $\frac { - 3 s - 24 } { 4 s + 29 }$ 
B)  $\frac { - 3 s + 24 } { 4 s + 29 }$ 
C)  $\frac { - 3 p - 24 } { 4 p + 29 }$ 
D)  $\frac { 24 } { 35 }$ 
E)  $- \frac { 24 } { 29 }$

Question 20

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

Estimate the slope of the line.

Find $( f + g ) ( x )$ . $f ( x ) = - 8 x ^ { 2 } + 5 x - 2$ $g ( x ) = 4 x ^ { 2 } + 7 x + 4$

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

Determine whether the function is even, odd, or neither. $f ( x ) = 4 x ^ { 3 } - 2 x$

Given that $f ( x ) = \sqrt [ 4 ] { x - 4 }$ and $g ( x ) = x ^ { 4 } + 4$ determine the value of the following (if possible). $( f \circ g ) ( 0 )$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 1$ and $g ( x ) = x - 6$ . $( f g ) ( - 2 )$

Find the slope and $y$ -intercept of the equation of the line. $y = - 2 x + 3$

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

Evaluate the following function at the specified value of the independent variable and simplify. $f ( u ) = \frac { 4 u ^ { 2 } + 12 } { u ^ { 2 } } ; \quad f ( 0 )$

Find $f \circ g$ . $f ( x ) = - 4 x + 3$

Use the graph of $f$ to sketch the graph of the function indicated below.

Evaluate the following function for $f ( x ) = - 2 x ^ { 2 } + 1$ and $g ( x ) = x + 4$ algebraically. $\left( \frac { f } { g } \right) ( q - 4 )$

Find $( f - g ) ( x )$ . $f ( x ) = - \frac { 8 x } { 4 x + 7 } \quad g ( x ) = - \frac { 4 } { x }$

Match the graph of the function shown below with the graph of its inverse function

Use the graphs of $y = f ( x )$ and $y = g ( x )$ to evaluate $\left( g ^ { - 1 } \circ f ^ { - 1 } \right) ( - 4 )$ $Use the graphs of y = f ( x ) and y = g ( x ) to evaluate \left( g ^ { - 1 } \circ f ^ { - 1 } \right) ( - 4 )$

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: $( - 4,7 )$ line: $- 5 x - 15 y = - 6$

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 49 }$ .

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( x + 4 )$

Evaluate the function at the specified value of the independent variable and simplify. f(p)= f(s+8)

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

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

Limits and an Introduction to Calculus

Filters

Exam 1: Functions and Their Graphs

Estimate the slope of the line.

Find (f+g)(x)( f + g ) ( x )(f+g)(x) . f(x)=−8x2+5x−2f ( x ) = - 8 x ^ { 2 } + 5 x - 2f(x)=−8x2+5x−2 g(x)=4x2+7x+4g ( x ) = 4 x ^ { 2 } + 7 x + 4g(x)=4x2+7x+4

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

Determine whether the function is even, odd, or neither. f(x)=4x3−2xf ( x ) = 4 x ^ { 3 } - 2 xf(x)=4x3−2x

Given that f(x)=x−44f ( x ) = \sqrt [ 4 ] { x - 4 }f(x)=4x−4​ and g(x)=x4+4g ( x ) = x ^ { 4 } + 4g(x)=x4+4 determine the value of the following (if possible). (f∘g)(0)( f \circ g ) ( 0 )(f∘g)(0)

Evaluate the indicated function for f(x)=x2−1f ( x ) = x ^ { 2 } - 1f(x)=x2−1 and g(x)=x−6g ( x ) = x - 6g(x)=x−6 . (fg)(−2)( f g ) ( - 2 )(fg)(−2)

Find the slope and yyy -intercept of the equation of the line. y=−2x+3y = - 2 x + 3y=−2x+3

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)

Evaluate the following function at the specified value of the independent variable and simplify. f(u)=4u2+12u2;f(0)f ( u ) = \frac { 4 u ^ { 2 } + 12 } { u ^ { 2 } } ; \quad f ( 0 )f(u)=u24u2+12​;f(0)

Find f∘gf \circ gf∘g . f(x)=−4x+3f ( x ) = - 4 x + 3f(x)=−4x+3

Use the graph of fff to sketch the graph of the function indicated below.

Evaluate the following function for f(x)=−2x2+1f ( x ) = - 2 x ^ { 2 } + 1f(x)=−2x2+1 and g(x)=x+4g ( x ) = x + 4g(x)=x+4 algebraically. (fg)(q−4)\left( \frac { f } { g } \right) ( q - 4 )(gf​)(q−4)

Find (f−g)(x)( f - g ) ( x )(f−g)(x) . f(x)=−8x4x+7g(x)=−4xf ( x ) = - \frac { 8 x } { 4 x + 7 } \quad g ( x ) = - \frac { 4 } { x }f(x)=−4x+78x​g(x)=−x4​

Match the graph of the function shown below with the graph of its inverse function

Use the graphs of y=f(x)y = f ( x )y=f(x) and y=g(x)y = g ( x )y=g(x) to evaluate (g−1∘f−1)(−4)\left( g ^ { - 1 } \circ f ^ { - 1 } \right) ( - 4 )(g−1∘f−1)(−4)

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: (−4,7)( - 4,7 )(−4,7) line: −5x−15y=−6- 5 x - 15 y = - 6−5x−15y=−6

Determine the domain of g(x)=1x2−49g ( x ) = \frac { 1 } { x ^ { 2 } - 49 }g(x)=x2−491​ .

If fff is an even function, determine if ggg is even, odd, or neither. g(x)=f(x+4)g ( x ) = f ( x + 4 )g(x)=f(x+4)

Evaluate the function at the specified value of the independent variable and simplify. f(p)= f(s+8)

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

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

Limits and an Introduction to Calculus

Filters

Find $( f + g ) ( x )$ . $f ( x ) = - 8 x ^ { 2 } + 5 x - 2$ $g ( x ) = 4 x ^ { 2 } + 7 x + 4$

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

Determine whether the function is even, odd, or neither. $f ( x ) = 4 x ^ { 3 } - 2 x$

Given that $f ( x ) = \sqrt [ 4 ] { x - 4 }$ and $g ( x ) = x ^ { 4 } + 4$ determine the value of the following (if possible). $( f \circ g ) ( 0 )$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 1$ and $g ( x ) = x - 6$ . $( f g ) ( - 2 )$

Find the slope and $y$ -intercept of the equation of the line. $y = - 2 x + 3$

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

Evaluate the following function at the specified value of the independent variable and simplify. $f ( u ) = \frac { 4 u ^ { 2 } + 12 } { u ^ { 2 } } ; \quad f ( 0 )$

Find $f \circ g$ . $f ( x ) = - 4 x + 3$

Use the graph of $f$ to sketch the graph of the function indicated below.

Evaluate the following function for $f ( x ) = - 2 x ^ { 2 } + 1$ and $g ( x ) = x + 4$ algebraically. $\left( \frac { f } { g } \right) ( q - 4 )$

Find $( f - g ) ( x )$ . $f ( x ) = - \frac { 8 x } { 4 x + 7 } \quad g ( x ) = - \frac { 4 } { x }$

Use the graphs of $y = f ( x )$ and $y = g ( x )$ to evaluate $\left( g ^ { - 1 } \circ f ^ { - 1 } \right) ( - 4 )$ $Use the graphs of y = f ( x ) and y = g ( x ) to evaluate \left( g ^ { - 1 } \circ f ^ { - 1 } \right) ( - 4 )$

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: $( - 4,7 )$ line: $- 5 x - 15 y = - 6$

Determine the domain of $g ( x ) = \frac { 1 } { x ^ { 2 } - 49 }$ .

If $f$ is an even function, determine if $g$ is even, odd, or neither. $g ( x ) = f ( x + 4 )$

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