Question 1

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: $- 3$ C

Question 2

Use the functions $f ( x ) = x + 4$ and $g ( x ) = 5 x - 7$ to find $( g \circ f ) ^ { - 1 }$.

Accepted Answer

A)  $( g \circ f ) ^ { - 1 } = \frac { 5 x + 11 } { 4 }$ 
B)  $( g \circ f ) ^ { - 1 } = 5 x - 42$ 
C)  $( g \circ f ) ^ { - 1 } = \frac { x - 13 } { 5 }$ 
D)  $( g \circ f ) ^ { - 1 } = \frac { - 7 x - 7 } { 5 }$ 
E)  $( g \circ f ) ^ { - 1 } = 5 x + 13$ 
A)  $( g \circ f ) ^ { - 1 } = \frac { 5 x + 11 } { 4 }$ 
B)  $( g \circ f ) ^ { - 1 } = 5 x - 42$ 
C)  $( g \circ f ) ^ { - 1 } = \frac { x - 13 } { 5 }$ 
D)  $( g \circ f ) ^ { - 1 } = \frac { - 7 x - 7 } { 5 }$ 
E)  $( g \circ f ) ^ { - 1 } = 5 x + 13$ C

Question 3

If f is an even function, determine if g is even, odd, or neither. $$g ( x ) = - f ( x + 3 )$$

Accepted Answer

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

Question 4

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 5

Hooke's Law states that the force $F$ required to compress or stretch a spring (within its elastic limits) is proportional to the distance $d$ that the spring is compressed or stretched from its original length. That is, $F = k d$, where $k$ is the measure of the stiffness of the spring and is called the spring constant. The table below shows the elongation $d$ in centimeters of a spring when a force of $F$ kilograms is applied.
$\begin{array}{|c|c|}
\hline \text { Force, } \boldsymbol{F} & \text { Elongation, } \boldsymbol{d} \
\hline 20 & 2.8 \
\hline 40 & 5.0 \
\hline 60 & 8.0 \
\hline 80 & 10.6 \
\hline 100 & 13.2 \
\hline
\end{array}$

Find the equation of the line that seems to best fit the data. Use the model to estimate the elongation of the spring when a force of 50 kilograms is applied. Round your answer to one decimal place.

Accepted Answer

A)  $13.2$ centimeters 
B)  $9.9$ centimeters 
C)  $3.3$ centimeters 
D)  $6.6$ centimeters 
E)  $5.0$ centimeters 
A)  $13.2$ centimeters 
B)  $9.9$ centimeters 
C)  $3.3$ centimeters 
D)  $6.6$ centimeters 
E)  $5.0$ centimeters

Question 6

Find $f \circ g$.
$f ( x ) = - 4 x + 3 \quad g ( x ) = x + 7$

Accepted Answer

A)  $( f \circ g ) ( x ) = - 4 x - 25$ 
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)  $( f \circ g ) ( x ) = - 5 x + 10$ 
A)  $( f \circ g ) ( x ) = - 4 x - 25$ 
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)  $( f \circ g ) ( x ) = - 5 x + 10$

Question 7

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 8

Find the value(s) of $x$ for which $f ( x ) = g ( x )$.
$f ( x ) = x ^ { 2 } - 11 x - 36 \quad g ( x ) = - 7 x - 4$

Accepted Answer

A)  $- 36 , - 25 , - \frac { 4 } { 7 }$ 
B)  $- 36 , - 11 , - \frac { 4 } { 7 }$ 
C)  $8 , - 4$ 
D)  $- 8,4$ 
E)  $47 , - \frac { 4 } { 7 }$ 
A)  $- 36 , - 25 , - \frac { 4 } { 7 }$ 
B)  $- 36 , - 11 , - \frac { 4 } { 7 }$ 
C)  $8 , - 4$ 
D)  $- 8,4$ 
E)  $47 , - \frac { 4 } { 7 }$

Question 9

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 10

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

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 11

Does the table describe a function? 
$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Input value } & - 6 & - 3 & 0 & 3 & 6 \
\hline \text { Output value } & 11 & 11 & 11 & 11 & 11 \
\hline
\end{array}$

Accepted Answer

A) True 
 B)False

Question 12

Evaluate the following function at the specified value of the independent variable and simplify. $f ( w ) = \frac { - 7 w ^ { 2 } + 20 } { w ^ { 2 } }$ ; $f(0)$

Accepted Answer

A)  20 
B)  0 
C)  -7 
D)  13 
E)  undefined 
A)  20 
B)  0 
C)  -7 
D)  13 
E)  undefined

Question 13

Compare the graph of the following function with the graph of $f ( x ) = \sqrt { x }$. $y = \sqrt { - x + 4 }$

Accepted Answer

A)  First a vertical shift of 4 units up then a reflection in the $y$-axis. 
B)  First a horizontal shift of 4 units to the left then a reflection in the $y$-axis. 
C)  First a vertical shift of 4 units up then a reflection in the $x$-axis. 
D)  First a horizontal shift of 4 units to the left, then a vertical shift of 4 units up and then a reflection in the $y$-axis. 
E)  First a horizontal shift of 4 units to the left then a reflection in the $x$-axis. 
A)  First a vertical shift of 4 units up then a reflection in the $y$-axis. 
B)  First a horizontal shift of 4 units to the left then a reflection in the $y$-axis. 
C)  First a vertical shift of 4 units up then a reflection in the $x$-axis. 
D)  First a horizontal shift of 4 units to the left, then a vertical shift of 4 units up and then a reflection in the $y$-axis. 
E)  First a horizontal shift of 4 units to the left then a reflection in the $x$-axis.

Question 14

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 15

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 16

Determine whether lines $L _ { 1 }$ and $L _ { 2 }$ passing through the pairs of points are parallel, perpendicular, or neither.
$L _ { 1 } : ( - 1,1 ) , ( - 1 , - 6 )$
$L _ { 2 } : ( 3 , - 8 ) , ( 24 , - 8 )$

Accepted Answer

A)  parallel 
B)  perpendicular 
C)  neither 
A)  parallel 
B)  perpendicular 
C)  neither

Question 17

Find the value(s) of $x$ for which $f ( x ) = g ( x )$.
$f ( x ) = x ^ { 2 } - 13 x + 5 \quad g ( x ) = - 9 x + 2$

Accepted Answer

A)  $5,18 , \frac { 2 } { 9 }$ 
B)  $5 , - 13 , \frac { 2 } { 9 }$ 
C)  3,1 
D)  $- 3 , - 1$ 
E)  $8 , \frac { 2 } { 9 }$ 
A)  $5,18 , \frac { 2 } { 9 }$ 
B)  $5 , - 13 , \frac { 2 } { 9 }$ 
C)  3,1 
D)  $- 3 , - 1$ 
E)  $8 , \frac { 2 } { 9 }$

Question 18

Compare the graph of the following function with the graph of $f ( x ) = x ^ { 3 }$.
$y = [ 5 ( x - 2 ) ] ^ { 3 }$

Accepted Answer

A)  vertical shift of 2 units down  vertical shift of 2 units down 
B)  horizontal shrink of $\frac { 1 } { 5 }$ units  horizontal shift of 2 units to the right 
C)  horizontal shrink of $\frac { 1 } { 125 }$ units horizontal shift of 2 units to the right 
D)  horizontal stretch of $\frac { 1 } { 5 }$ units 
E)  horizontal shift of 2 units to the right vertical shift of 5 units down 
A)  vertical shift of 2 units down  vertical shift of 2 units down 
B)  horizontal shrink of $\frac { 1 } { 5 }$ units  horizontal shift of 2 units to the right 
C)  horizontal shrink of $\frac { 1 } { 125 }$ units horizontal shift of 2 units to the right 
D)  horizontal stretch of $\frac { 1 } { 5 }$ units 
E)  horizontal shift of 2 units to the right vertical shift of 5 units down

Question 19

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 5$ and $g ( x ) = x + 9$
$( f g ) ( - 1 )$

Accepted Answer

A)  $- 32$ 
B)  $- 48$ 
C)  $- 46$ 
D)  40 
E)  $- 50$ 
A)  $- 32$ 
B)  $- 48$ 
C)  $- 46$ 
D)  40 
E)  $- 50$

Question 20

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant.
$$f ( x ) = - x ^ { 3 } + 3 x + 1$$

Accepted Answer

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

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

Use the functions $f ( x ) = x + 4$ and $g ( x ) = 5 x - 7$ to find $( g \circ f ) ^ { - 1 }$ .

If f is an even function, determine if g is even, odd, or neither. $g ( x ) = - f ( x + 3 )$

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

Find $f \circ g$ . $f ( x ) = - 4 x + 3 \quad g ( x ) = x + 7$

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

Find the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 11 x - 36 \quad g ( x ) = - 7 x - 4$

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

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

Does the table describe a function? Input value -6 -3 0 3 6 Output value 11 11 11 11 11

Evaluate the following function at the specified value of the independent variable and simplify. $f ( w ) = \frac { - 7 w ^ { 2 } + 20 } { w ^ { 2 } }$ ; $f(0)$

Compare the graph of the following function with the graph of $f ( x ) = \sqrt { x }$ . $y = \sqrt { - x + 4 }$

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

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

Determine whether lines $L _ { 1 }$ and $L _ { 2 }$ passing through the pairs of points are parallel, perpendicular, or neither. $L _ { 1 } : ( - 1,1 ) , ( - 1 , - 6 )$ $L _ { 2 } : ( 3 , - 8 ) , ( 24 , - 8 )$

Find the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 13 x + 5 \quad g ( x ) = - 9 x + 2$

Compare the graph of the following function with the graph of $f ( x ) = x ^ { 3 }$ . $y = [ 5 ( x - 2 ) ] ^ { 3 }$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 5$ and $g ( x ) = x + 9$ $( f g ) ( - 1 )$

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. $f ( x ) = - x ^ { 3 } + 3 x + 1$

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

Review of Graphs, Equations, and Inequalities

Filters

Exam 1: Functions and Their Graphs

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

Use the functions f(x)=x+4f ( x ) = x + 4f(x)=x+4 and g(x)=5x−7g ( x ) = 5 x - 7g(x)=5x−7 to find (g∘f)−1( g \circ f ) ^ { - 1 }(g∘f)−1 .

If f is an even function, determine if g is even, odd, or neither. g(x)=−f(x+3)g ( x ) = - f ( x + 3 )g(x)=−f(x+3)

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

Find f∘gf \circ gf∘g . f(x)=−4x+3g(x)=x+7f ( x ) = - 4 x + 3 \quad g ( x ) = x + 7f(x)=−4x+3g(x)=x+7

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

Find the value(s) of xxx for which f(x)=g(x)f ( x ) = g ( x )f(x)=g(x) . f(x)=x2−11x−36g(x)=−7x−4f ( x ) = x ^ { 2 } - 11 x - 36 \quad g ( x ) = - 7 x - 4f(x)=x2−11x−36g(x)=−7x−4

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)

Evaluate the function at the specified value of the independent variable and simplify. f(p)=−3p4p−3f ( p ) = \frac { - 3 p } { 4 p - 3 }f(p)=4p−3−3p​ , f′(s+8)f ^ { \prime } ( s + 8 )f′(s+8)

Does the table describe a function? Input value -6 -3 0 3 6 Output value 11 11 11 11 11

Evaluate the following function at the specified value of the independent variable and simplify. f(w)=−7w2+20w2f ( w ) = \frac { - 7 w ^ { 2 } + 20 } { w ^ { 2 } }f(w)=w2−7w2+20​ ; f(0)f(0)f(0)

Compare the graph of the following function with the graph of f(x)=xf ( x ) = \sqrt { x }f(x)=x​ . y=−x+4y = \sqrt { - x + 4 }y=−x+4​

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 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 the value(s) of xxx for which f(x)=g(x)f ( x ) = g ( x )f(x)=g(x) . f(x)=x2−13x+5g(x)=−9x+2f ( x ) = x ^ { 2 } - 13 x + 5 \quad g ( x ) = - 9 x + 2f(x)=x2−13x+5g(x)=−9x+2

Compare the graph of the following function with the graph of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 . y=[5(x−2)]3y = [ 5 ( x - 2 ) ] ^ { 3 }y=[5(x−2)]3

Evaluate the indicated function for f(x)=x2−5f ( x ) = x ^ { 2 } - 5f(x)=x2−5 and g(x)=x+9g ( x ) = x + 9g(x)=x+9 (fg)(−1)( f g ) ( - 1 )(fg)(−1)

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. f(x)=−x3+3x+1f ( x ) = - x ^ { 3 } + 3 x + 1f(x)=−x3+3x+1

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

Review of Graphs, Equations, and Inequalities

Filters

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

Use the functions $f ( x ) = x + 4$ and $g ( x ) = 5 x - 7$ to find $( g \circ f ) ^ { - 1 }$ .

If f is an even function, determine if g is even, odd, or neither. $g ( x ) = - f ( x + 3 )$

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

Find $f \circ g$ . $f ( x ) = - 4 x + 3 \quad g ( x ) = x + 7$

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

Find the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 11 x - 36 \quad g ( x ) = - 7 x - 4$

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

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

Evaluate the following function at the specified value of the independent variable and simplify. $f ( w ) = \frac { - 7 w ^ { 2 } + 20 } { w ^ { 2 } }$ ; $f(0)$

Compare the graph of the following function with the graph of $f ( x ) = \sqrt { x }$ . $y = \sqrt { - x + 4 }$

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

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 the value(s) of $x$ for which $f ( x ) = g ( x )$ . $f ( x ) = x ^ { 2 } - 13 x + 5 \quad g ( x ) = - 9 x + 2$

Compare the graph of the following function with the graph of $f ( x ) = x ^ { 3 }$ . $y = [ 5 ( x - 2 ) ] ^ { 3 }$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } - 5$ and $g ( x ) = x + 9$ $( f g ) ( - 1 )$

Use a graphing utility to graph the function and visually determine the intervals over which the function is increasing, decreasing, or constant. $f ( x ) = - x ^ { 3 } + 3 x + 1$