Question 1

Determine the intervals of the domain over which the function is continuous.
-

Accepted Answer

A)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  $( - \infty , 1 ) \cup ( 1 , \infty )$ 
C)  $( - \infty , 1 ] \cup [ 1 , \infty )$ 
D)  $( - \infty , \infty )$ 
A)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  $( - \infty , 1 ) \cup ( 1 , \infty )$ 
C)  $( - \infty , 1 ] \cup [ 1 , \infty )$ 
D)  $( - \infty , \infty )$

Question 2

Decide whether the relation defines a function.
-

Accepted Answer

A)  Not a function 
B)  Function 
A)  Not a function 
B)  Function

Question 3

Decide whether the relation defines a function.
-$y ^ { 2 } = 2 x$

Accepted Answer

A)  Function 
B)  Not a function 
A)  Function 
B)  Not a function

Question 4

Compute and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$
-$$f ( x ) = \frac { 20 } { x + 15 }$$

Accepted Answer

A)  $\frac { 20 } { ( x + h + 15 ) ( x + 15 ) }$ 
B)  $- \frac { 20 } { ( x + 20 ) ^ { 2 } }$ 
C)  $- \frac { 20 } { ( x + h + 15 ) ( x + 15 ) }$ 
D)  $- \frac { 300 } { ( x + h + 15 ) ( x + 15 ) }$ 
A)  $\frac { 20 } { ( x + h + 15 ) ( x + 15 ) }$ 
B)  $- \frac { 20 } { ( x + 20 ) ^ { 2 } }$ 
C)  $- \frac { 20 } { ( x + h + 15 ) ( x + 15 ) }$ 
D)  $- \frac { 300 } { ( x + h + 15 ) ( x + 15 ) }$

Question 5

Match the equation with the correct graph.
-$$y = \frac { 1 } { 2 } x - 2$$

Accepted Answer

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

Question 6

List the ordered pairs from the table.
-
$\begin{array}{c|r}
x & y \
\hline-5 & -7 \
-4 & -5 \
-2 & -1 \
-1 & 1
\end{array}$

Accepted Answer

A)  $( - 5,1 ) , ( - 4 , - 1 ) , ( - 2 , - 5 ) , ( - 1 , - 7 )$ 
B)  $( - 7 , - 5 ) , ( - 5 , - 4 ) , ( - 1 , - 2 ) , ( 1 , - 1 )$ 
C)  $( - 5 , - 7 ) , ( - 4 , - 5 ) , ( - 2 , - 1 ) , ( - 1,1 )$ 
D)  $( - 5 , - 5 ) , ( - 4 , - 7 ) , ( - 2,1 ) , ( - 1 , - 1 )$ 
A)  $( - 5,1 ) , ( - 4 , - 1 ) , ( - 2 , - 5 ) , ( - 1 , - 7 )$ 
B)  $( - 7 , - 5 ) , ( - 5 , - 4 ) , ( - 1 , - 2 ) , ( 1 , - 1 )$ 
C)  $( - 5 , - 7 ) , ( - 4 , - 5 ) , ( - 2 , - 1 ) , ( - 1,1 )$ 
D)  $( - 5 , - 5 ) , ( - 4 , - 7 ) , ( - 2,1 ) , ( - 1 , - 1 )$

Question 7

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$
-Select the equation that describes the graph shown.

Accepted Answer

A)  $y = - 2 ( x - 5 ) ^ { 2 } + 2$ 
B)  $y = - 2 ( x + 5 ) ^ { 2 }$ 
C)  $y = - 2 ( x - 5 ) ^ { 2 }$ 
D)  $y = - 2 x ^ { 2 } - 5$ 
A)  $y = - 2 ( x - 5 ) ^ { 2 } + 2$ 
B)  $y = - 2 ( x + 5 ) ^ { 2 }$ 
C)  $y = - 2 ( x - 5 ) ^ { 2 }$ 
D)  $y = - 2 x ^ { 2 } - 5$

Question 8

Write all linear equations in slope-intercept form.
-A biologist recorded 8 snakes on 23 acres in one area and 16 snakes on 37 acres in another area. Find a linear equation that models the number of snakes in x acres.

Accepted Answer

A)  $y = x + 15$ 
B)  $y = \frac { 4 } { 7 } x - \frac { 36 } { 7 }$ 
C)  $y = \frac { 4 } { 7 } x + \frac { 36 } { 7 }$ 
D)  $y = \frac { 7 } { 4 } x - \frac { 7 } { 36 }$ 
A)  $y = x + 15$ 
B)  $y = \frac { 4 } { 7 } x - \frac { 36 } { 7 }$ 
C)  $y = \frac { 4 } { 7 } x + \frac { 36 } { 7 }$ 
D)  $y = \frac { 7 } { 4 } x - \frac { 7 } { 36 }$

Question 9

Find the requested value.
-$f ( - 8 )$ for $f ( x ) = \left\{ \begin{array} { l l } 6 x + 1 , & \text { if } x  12 \end{array} \right.$

Accepted Answer

A)  64 
B)  $- 47$ 
C)  $- 64$ 
D)  49 
A)  64 
B)  $- 47$ 
C)  $- 64$ 
D)  49

Question 10

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$\mathrm { P } ( - \sqrt { 10 } , 1 ) , \mathrm { Q } ( 0 , \sqrt { 3 } )$

Accepted Answer

A)  $\left( - \frac { \sqrt { 10 } } { 2 } , \frac { 1 + \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( \frac { \sqrt { 10 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } \right)$ 
C)  $( - \sqrt { 10 } , 1 + \sqrt { 3 } )$ 
D)  $\left\{ \frac { - \sqrt { 10 } + \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$ 
A)  $\left( - \frac { \sqrt { 10 } } { 2 } , \frac { 1 + \sqrt { 3 } } { 2 } \right)$ 
B)  $\left( \frac { \sqrt { 10 } } { 2 } , \frac { 1 - \sqrt { 3 } } { 2 } \right)$ 
C)  $( - \sqrt { 10 } , 1 + \sqrt { 3 } )$ 
D)  $\left\{ \frac { - \sqrt { 10 } + \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right)$

Question 11

Compute and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$
-$$f ( x ) = \frac { x - 9 } { x + 3 }$$

Accepted Answer

A)  $\frac { 12 } { ( x + h + 3 ) ( x + 3 ) }$ 
B)  $\frac { 13 } { ( x + 3 ) ( x - 3 ) }$ 
C)  $\frac { 12 ( x + h + 3 ) } { ( x + 3 ) }$ 
D)  $- \frac { 12 } { x ( x + 3 ) }$ 
A)  $\frac { 12 } { ( x + h + 3 ) ( x + 3 ) }$ 
B)  $\frac { 13 } { ( x + 3 ) ( x - 3 ) }$ 
C)  $\frac { 12 ( x + h + 3 ) } { ( x + 3 ) }$ 
D)  $- \frac { 12 } { x ( x + 3 ) }$

Question 12

Find the center and radius of the circle.
-$$2 x ^ { 2 } + 2 y ^ { 2 } - 16 x - 4 y + 16 = 0$$

Accepted Answer

A)  center: $( 4,1 )$, radius: 3 
B)  center: $( 1,4 )$, radius: 3 
C)  center: $( - 4 , - 1 )$, radius: 9 
D)  center: $( - 1 , - 4 )$, radius: 9 
A)  center: $( 4,1 )$, radius: 3 
B)  center: $( 1,4 )$, radius: 3 
C)  center: $( - 4 , - 1 )$, radius: 9 
D)  center: $( - 1 , - 4 )$, radius: 9

Question 13

Find the average rate of change illustrated in the graph.
-  Time (in hours)

Accepted Answer

A)  $0.2$ miles per hour 
B)  $2.5$ miles per hour 
C)  5 miles per hour 
D)  25 miles per hour 
A)  $0.2$ miles per hour 
B)  $2.5$ miles per hour 
C)  5 miles per hour 
D)  25 miles per hour

Question 14

Evaluate the function.
-Find $f ( 3 )$ when $f ( x ) = x ^ { 2 } - 2 x - 5$

Accepted Answer

A)  $- 2$ 
B)  20 
C)  10 
D)  8 
A)  $- 2$ 
B)  20 
C)  10 
D)  8

Question 15

Match the description with the correct symbolic expression.
-a function that is not linear

Accepted Answer

A)  f(x) = x - 9 
B)  f(x) = -2 
C)  f(x) = 6x + 4 
D)  f(x) = -9x + 6 
A)  f(x) = x - 9 
B)  f(x) = -2 
C)  f(x) = 6x + 4 
D)  f(x) = -9x + 6

Question 16

Graph the line and give the domain and the range.
-$y+1=0$

Accepted Answer

A)  $D = ( - \infty , \infty ) , R = \{ - 1 \}$
  
B)  $D = ( - \infty , \infty ) , R = \{ - 1 \}$
  
C)   $D=(-\infty, \infty), R=(-\infty, \infty)$
  
D)   $D=\{-1\}, R=(-\infty, \infty)$

Question 17

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function.
-The reflection of the graph of $y = f ( x )$ across the $x$-axis

Accepted Answer

A)  $( 2 , - 4 )$ 
B)  $( - 2 , - 4 )$ 
C)  $( - 2,4 )$ 
D)  $( 2,4 )$ 
A)  $( 2 , - 4 )$ 
B)  $( - 2 , - 4 )$ 
C)  $( - 2,4 )$ 
D)  $( 2,4 )$

Question 18

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = \sqrt { 2 x + 2 } , g ( x ) = \sqrt { 9 x - 25 }$$
Find $( \mathrm { fg } ) ( \mathrm { x } )$.

Accepted Answer

A)  $( \sqrt { 2 x + 2 } ) ( \sqrt { 9 x - 25 } )$ 
B)  $( 3 x - 5 ) ( \sqrt { 2 x + 2 } )$ 
C)  $( 2 x + 2 ) ( 3 x - 5 )$ 
D)  $( 2 x + 2 ) ( 9 x - 25 )$ 
A)  $( \sqrt { 2 x + 2 } ) ( \sqrt { 9 x - 25 } )$ 
B)  $( 3 x - 5 ) ( \sqrt { 2 x + 2 } )$ 
C)  $( 2 x + 2 ) ( 3 x - 5 )$ 
D)  $( 2 x + 2 ) ( 9 x - 25 )$

Question 19

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (0, 3), endpoint (-4, 8)

Accepted Answer

A)  (4, 13) 
B)  (4, -2) 
C)  (-14, 16) 
D)  (-12, 18) 
A)  (4, 13) 
B)  (4, -2) 
C)  (-14, 16) 
D)  (-12, 18)

Question 20

Give the domain and range of the relation.
-

Accepted Answer

A)  range: $( - 3,3 )$; domain: $( - 10,10 )$ 
B)  range: $( - \infty , - 3 ) \cup ( - 3,0 ) \cup ( 0,3 ) \cup ( 3 , \infty )$; domain: $( - \infty , - 10 ) \cup ( - 10,0 ) \cup ( 0,10 ) \cup ( 10 , \infty )$ 
C)  range: $( - 3,0 ) \cup ( 0,3 )$; domain: $( - 10,0 ) \cup ( 0,10 )$ 
D)  range: $( - \infty , \infty )$; domain: $( - \infty , \infty )$ 
A)  range: $( - 3,3 )$; domain: $( - 10,10 )$ 
B)  range: $( - \infty , - 3 ) \cup ( - 3,0 ) \cup ( 0,3 ) \cup ( 3 , \infty )$; domain: $( - \infty , - 10 ) \cup ( - 10,0 ) \cup ( 0,10 ) \cup ( 10 , \infty )$ 
C)  range: $( - 3,0 ) \cup ( 0,3 )$; domain: $( - 10,0 ) \cup ( 0,10 )$ 
D)  range: $( - \infty , \infty )$; domain: $( - \infty , \infty )$

Determine the intervals of the domain over which the function is continuous. -

Decide whether the relation defines a function. -

Decide whether the relation defines a function. - $y ^ { 2 } = 2 x$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = \frac { 20 } { x + 15 }$

Match the equation with the correct graph. - $y = \frac { 1 } { 2 } x - 2$

List the ordered pairs from the table. - x y -5 -7 -4 -5 -2 -1 -1 1

Describe how the graph of the equation relates to the graph of y $y = \sqrt [ 3 ] { x }$ -Select the equation that describes the graph shown. $Describe how the graph of the equation relates to the graph of y y = \sqrt [ 3 ] { x } -Select the equation that describes the graph shown.$

Write all linear equations in slope-intercept form. -A biologist recorded 8 snakes on 23 acres in one area and 16 snakes on 37 acres in another area. Find a linear equation that models the number of snakes in x acres.

Find the requested value. - $f ( - 8 )$ for $f ( x ) = \left\{ \begin{array} { l l } 6 x + 1 , & \text { if } x < 8 \\ 8 x , & \text { if } 8 \leq x \leq 12 \\ 8 - 7 x , & \text { if } x > 12 \end{array} \right.$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( - \sqrt { 10 } , 1 ) , \mathrm { Q } ( 0 , \sqrt { 3 } )$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = \frac { x - 9 } { x + 3 }$

Find the center and radius of the circle. - $2 x ^ { 2 } + 2 y ^ { 2 } - 16 x - 4 y + 16 = 0$

Find the average rate of change illustrated in the graph. - Time (in hours)

Evaluate the function. -Find $f ( 3 )$ when $f ( x ) = x ^ { 2 } - 2 x - 5$

Match the description with the correct symbolic expression. -a function that is not linear

Graph the line and give the domain and the range. - $y+1=0$

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of $y = f ( x )$ across the $x$ -axis

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = \sqrt { 2 x + 2 } , g ( x ) = \sqrt { 9 x - 25 }$ Find $( \mathrm { fg } ) ( \mathrm { x } )$ .

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (0, 3), endpoint (-4, 8)

Give the domain and range of the relation. -

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