Question 1

Write an equation for the line described. Give your answer in slope-intercept form.
-$m = 5$, through $( 4 , - 8 )$

Accepted Answer

A)  $y = 6 x + 29$ 
B)  $y = 5 x - 28$ 
C)  $y = 5 x + 27$ 
D)  $y = 5 x - 26$ 
A)  $y = 6 x + 29$ 
B)  $y = 5 x - 28$ 
C)  $y = 5 x + 27$ 
D)  $y = 5 x - 26$

Question 2

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant.
-

Accepted Answer

A)  Increasing $( 0 , \infty )$; Decreasing $( - \infty , 0 )$ 
B)  Increasing for all reals; Decreasing never 
C)  Increasing never; Decreasing for all reals 
D)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , \infty )$ 
A)  Increasing $( 0 , \infty )$; Decreasing $( - \infty , 0 )$ 
B)  Increasing for all reals; Decreasing never 
C)  Increasing never; Decreasing for all reals 
D)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , \infty )$

Question 3

Graph the function.
-$$f ( x ) = \left\{ \begin{array} { l l } 
x ^ { 2 } - 4 , & \text { if } x  1
\end{array} \right.$$

Accepted Answer

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

Question 4

Find the requested value.
-Using the given tables, find $( g \mathrm {~g} ) ( 4 )$
$\begin{array}{l}
\begin{array}{l|r|l|r|r}
\mathrm{x} & 4 & 7 & 5 & 10 \
\hline \mathrm{f}(\mathrm{x}) & 5 & 8 & 19 & 21
\end{array}\
\begin{array}{l|r|r|r|r}
\mathrm{x} & 6 & 10 & 4 & 5 \
\hline \mathrm{g}(\mathrm{x}) & 11 & 7 & 10 & 9
\end{array}
\end{array}$

Accepted Answer

A)  7 
B)  9 
C)  19 
D)  21 
A)  7 
B)  9 
C)  19 
D)  21

Question 5

Find the requested value.
-$f ( 8 )$ for $f ( x ) = \left\{ \begin{array} { l l } 8 x + 1 , & \text { if } x  11 \end{array} \right.$

Accepted Answer

A)  56 
B)  $- 32$ 
C)  64 
D)  9 
A)  56 
B)  $- 32$ 
C)  64 
D)  9

Question 6

For the points P and Q, find the distance d(P, Q).
-$\mathrm { P } ( 2,7 ) , \mathrm { Q } ( - 1 , - 3 )$

Accepted Answer

A)  $- 7$ 
B)  $\sqrt { 91 }$ 
C)  $\sqrt { 109 }$ 
D)  30 
A)  $- 7$ 
B)  $\sqrt { 91 }$ 
C)  $\sqrt { 109 }$ 
D)  30

Question 7

Find the specified domain.
-Use the graphs to find the value of $( f + g ) ( 3 )$.

Accepted Answer

A)  3 
B)  $- 1$ 
C)  1 
D)  0 
A)  3 
B)  $- 1$ 
C)  1 
D)  0

Question 8

Write an equation for the line described. Write the equation in the form specified.
-parallel to y + 5x = 4, through (3, 5); slope-intercept form

Accepted Answer

A)  $y = - 5 x - 20$ 
B)  $y = - 5 x + 20$ 
C)  $y = - \frac { 1 } { 5 } x - 4$ 
D)  $y = 5 x - 20$ 
A)  $y = - 5 x - 20$ 
B)  $y = - 5 x + 20$ 
C)  $y = - \frac { 1 } { 5 } x - 4$ 
D)  $y = 5 x - 20$

Question 9

Graph the point symmetric to the given point.
-$$\text { Plot the point } ( - 6 , - 9 ) \text {, then plot the point that is symmetric to } ( - 6 , - 9 ) \text { with respect to the } x \text {-axis. }$$

Accepted Answer

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

Question 10

Graph the function.
-Sketch a graph showing the distance (in miles) that a person is from home after x hours if that individual drives at 35 mph to a lake 70 miles away, stays at the lake 1.5 hours, and then returns
Home at a speed of 70 mph.

Accepted Answer

A)

B)  none of these 130 
C) 
  
D) 
  
A)

B)  none of these 130 
C) 
  
D)

Question 11

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = 4 x ^ { 2 } - 7 x , g ( x ) = x ^ { 2 } - 5 x - 14$$
Find $\left( \frac { f } { g } \right) ( x )$.

Accepted Answer

A)  $\frac { 4 x - 7 } { - 5 }$ 
B)  $\frac { 4 x } { x + 1 }$ 
C)  $\frac { 4 - \mathrm { x } } { 14 }$ 
D)  $\frac { 4 x ^ { 2 } - 7 x } { x ^ { 2 } - 5 x - 14 }$ 
A)  $\frac { 4 x - 7 } { - 5 }$ 
B)  $\frac { 4 x } { x + 1 }$ 
C)  $\frac { 4 - \mathrm { x } } { 14 }$ 
D)  $\frac { 4 x ^ { 2 } - 7 x } { x ^ { 2 } - 5 x - 14 }$

Question 12

Evaluate the function.
-Find $f ( - 2 )$ if $f = \{ ( - 2,3 ) , ( 3,0 ) , ( 0,5 ) , ( 5 , - 2 ) \}$

Accepted Answer

A)  None of these 
B)  $( 3,5 )$ 
C)  5 
D)  3 
A)  None of these 
B)  $( 3,5 )$ 
C)  5 
D)  3

Question 13

Find the slope of the line and sketch the graph.
-$$- 4 y = 3 x$$

Accepted Answer

A) $m=\frac{3}{4}$

B)  $m=-\frac{3}{4}$
  
C)  $\mathrm { m } = \frac { 4 } { 3 }$
  
D)  $m = - \frac { 4 } { 3 }$
  
A) $m=\frac{3}{4}$

B)  $m=-\frac{3}{4}$
  
C)  $\mathrm { m } = \frac { 4 } { 3 }$
  
D)  $m = - \frac { 4 } { 3 }$

Question 14

Refer to the following graphs to determine an appropriate response.  
-Which one is the graph of $y = x ^ { 3 }$ ? What is its range?

Accepted Answer

A)  graph $C$; $[ - 2,2 ]$ 
B)  graph A; $( - \infty , \infty )$ 
C)  graph B; $( - \infty , \infty )$ 
D)  graph D; $[ 0 , \infty )$ 
A)  graph $C$; $[ - 2,2 ]$ 
B)  graph A; $( - \infty , \infty )$ 
C)  graph B; $( - \infty , \infty )$ 
D)  graph D; $[ 0 , \infty )$

Question 15

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to -9x + y = 5, through (5, 4); slope-intercept form

Accepted Answer

A)  $y = - \frac { 1 } { 9 } x - \frac { 41 } { 9 }$ 
B)  $y = - \frac { 1 } { 9 } x + \frac { 41 } { 9 }$ 
C)  $y = - 9 x - 41$ 
D)  $y = \frac { 1 } { 9 } x - \frac { 41 } { 9 }$ 
A)  $y = - \frac { 1 } { 9 } x - \frac { 41 } { 9 }$ 
B)  $y = - \frac { 1 } { 9 } x + \frac { 41 } { 9 }$ 
C)  $y = - 9 x - 41$ 
D)  $y = \frac { 1 } { 9 } x - \frac { 41 } { 9 }$

Question 16

Find the requested value.
-Using the given tables, find ( $g q ) ( 4 )$
$\begin{array}{l}
\begin{array}{l|l|l|r|r}
\mathrm{x} & 4 & 7 & 5 & 10 \
\hline \mathrm{f}(\mathrm{x}) & 5 & 8 & 19 & 21
\end{array}\
\begin{array}{l|r|r|r|r}
\mathrm{x} & 6 & 10 & 4 & 5 \
\hline \mathrm{g}(\mathrm{x}) & 11 & 7 & 10 & 9
\end{array}
\end{array}$

Accepted Answer

A)  7 
B)  19 
C)  4 
D)  9 
A)  7 
B)  19 
C)  4 
D)  9

Question 17

Evaluate the function.
-Find $f ( 5 )$ when $f ( x ) = 6 x - 3$

Accepted Answer

A)  3 
B)  27 
C)  33 
D)  15 
A)  3 
B)  27 
C)  33 
D)  15

Question 18

Find the average rate of change illustrated in the graph.
-

Accepted Answer

A)  $\$ 7000.00$ per year 
B)  $- \$ 6000.00$ per year 
C)  $\$ 6000.00$ per year 
D)  $- \$ 7000.00$ per year 
A)  $\$ 7000.00$ per year 
B)  $- \$ 6000.00$ per year 
C)  $\$ 6000.00$ per year 
D)  $- \$ 7000.00$ per year

Question 19

Find the requested value.
-Using the given tables, find find $(f \circ f)(2)$ 
$\begin{array}{l}
\begin{array}{l|l|l|l|l}
x & 2 & 5 & 3 & 1 \
\hline f(x) & 3 & 2 & 7 & 9
\end{array}\
\begin{array}{l|l|l|l|l}
\mathrm{x} & 4 & 2 & 5 & 3 \
\hline g(x) & 7 & 3 & 9 & 5
\end{array}
\end{array}$

Accepted Answer

A)  7 
B)  5 
C)  2 
D)  9 
A)  7 
B)  5 
C)  2 
D)  9

Question 20

For the given functions f and g , find the indicated composition.
-$$\begin{array} { l } 
f ( x ) = \frac { x - 8 } { 3 } , \quad g ( x ) = 3 x + 8 \
( g f ) ( x )
\end{array}$$

Accepted Answer

A)  $x - \frac { 8 } { 3 }$ 
B)  $x + 16$ 
C)  $x$ 
D)  $3 x + 16$ 
A)  $x - \frac { 8 } { 3 }$ 
B)  $x + 16$ 
C)  $x$ 
D)  $3 x + 16$

Write an equation for the line described. Give your answer in slope-intercept form. - $m = 5$ , through $( 4 , - 8 )$

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant. -

Find the requested value. -Using the given tables, find $( g \mathrm {~g} ) ( 4 )$ 4 7 5 10 () 5 8 19 21 6 10 4 5 () 11 7 10 9

Find the requested value. - $f ( 8 )$ for $f ( x ) = \left\{ \begin{array} { l l } 8 x + 1 , & \text { if } x < 1 \\ 8 x , & \text { if } 8 \leq x \leq 11 \\ 8 - 5 x , & \text { if } x > 11 \end{array} \right.$

For the points P and Q, find the distance d(P, Q). - $\mathrm { P } ( 2,7 ) , \mathrm { Q } ( - 1 , - 3 )$

Find the specified domain. -Use the graphs to find the value of $( f + g ) ( 3 )$ .

Write an equation for the line described. Write the equation in the form specified. -parallel to y + 5x = 4, through (3, 5); slope-intercept form

Graph the function. -Sketch a graph showing the distance (in miles) that a person is from home after x hours if that individual drives at 35 mph to a lake 70 miles away, stays at the lake 1.5 hours, and then returns Home at a speed of 70 mph.

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 4 x ^ { 2 } - 7 x , g ( x ) = x ^ { 2 } - 5 x - 14$ Find $\left( \frac { f } { g } \right) ( x )$ .

Evaluate the function. -Find $f ( - 2 )$ if $f = \{ ( - 2,3 ) , ( 3,0 ) , ( 0,5 ) , ( 5 , - 2 ) \}$

Find the slope of the line and sketch the graph. - $- 4 y = 3 x$

Refer to the following graphs to determine an appropriate response. $Refer to the following graphs to determine an appropriate response. -Which one is the graph of y = x ^ { 3 } ? What is its range?$ -Which one is the graph of $y = x ^ { 3 }$ ? What is its range?

Write an equation for the line described. Write the equation in the form specified. -perpendicular to -9x + y = 5, through (5, 4); slope-intercept form

Find the requested value. -Using the given tables, find ( $g q ) ( 4 )$ 4 7 5 10 () 5 8 19 21 6 10 4 5 () 11 7 10 9

Evaluate the function. -Find $f ( 5 )$ when $f ( x ) = 6 x - 3$

Find the average rate of change illustrated in the graph. -

Find the requested value. -Using the given tables, find find $(f \circ f)(2)$ x 2 5 3 1 f(x) 3 2 7 9 4 2 5 3 g(x) 7 3 9 5

For the given functions f and g , find the indicated composition. - f(x)=,g(x)=3x+8 (gf)(x)

Review of Basic Concepts

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 3: Graphs and Functions

Write an equation for the line described. Give your answer in slope-intercept form. - m=5m = 5m=5 , through (4,−8)( 4 , - 8 )(4,−8)