Question 1

Find the domain of the function.
-$$f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 15 }$$

Accepted Answer

A)  $( \infty , - 15 )$ or $( - 15 , \infty )$ 
B)  $( - 15 , \infty )$ 
C)  $( \infty , 0 )$ or $( 0 , \infty )$ 
D)  $( \infty , \infty )$ 
A)  $( \infty , - 15 )$ or $( - 15 , \infty )$ 
B)  $( - 15 , \infty )$ 
C)  $( \infty , 0 )$ or $( 0 , \infty )$ 
D)  $( \infty , \infty )$ D

Question 2

Express the interval in set builder notation and graph the interval on a number line.
-

Accepted Answer

A) domain: $ (0, \infty) $
      range: $ (\infty, \infty) $ 
B) domain: $ (\infty, \infty) $ 
range: $ (\infty, \infty) $ 
C)  domain: $ (\infty, \infty) $
 range:$0,\infty) $ 
D) domain: $ (0, \infty) $
range: $ (0, \infty) $ 
A) domain: $ (0, \infty) $
      range: $ (\infty, \infty) $ 
B) domain: $ (\infty, \infty) $ 
range: $ (\infty, \infty) $ 
C)  domain: $ (\infty, \infty) $
 range:$0,\infty) $ 
D) domain: $ (0, \infty) $
range: $ (0, \infty) $ B

Question 3

Decide whether the relation is a function.
-$$\{ ( - 7 , - 8 ) , ( - 5,8 ) , ( 1,5 ) , ( 3 , - 4 ) \}$$

Accepted Answer

A)  function 
B)  not a function 
A)  function 
B)  not a function A

Question 4

Find the domain of the function.
-$$f ( x ) = - 5 x + 9$$

Accepted Answer

A)  $( \infty , \infty )$ 
B)  $( \infty , - 9 )$ or $( - 9 , \infty )$ 
C)  $( \infty , 0 )$ or $( 0 , \infty )$ 
D)  $( - 9 , \infty )$ 
A)  $( \infty , \infty )$ 
B)  $( \infty , - 9 )$ or $( - 9 , \infty )$ 
C)  $( \infty , 0 )$ or $( 0 , \infty )$ 
D)  $( - 9 , \infty )$

Question 5

Find the indicated function value.
-Find $f ( 3 )$ when $f ( x ) = \frac { x ^ { 3 } + 6 } { x ^ { 2 } + 1 }$.

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B)  $\frac { 33 } { 10 }$ 
C)  $\frac { 11 } { 3 }$ 
D)  $\frac { 27 } { 10 }$ 
A)  $\frac { 3 } { 2 }$ 
B)  $\frac { 33 } { 10 }$ 
C)  $\frac { 11 } { 3 }$ 
D)  $\frac { 27 } { 10 }$

Question 6

Find the indicated function value.
-$$\begin{array} { l } 
f ( x ) = 3 x ^ { 2 } - 4 , g ( x ) = 2 x ^ { 2 } + 4 x - 1 \
\text { Find } ( f + g ) ( 5 )
\end{array}$$

Accepted Answer

A)  142 
B)  140 
C)  100 
D)  80 
A)  142 
B)  140 
C)  100 
D)  80

Question 7

Express the interval in set builder notation and graph the interval on a number line.
-$( - 9,4 )$

Accepted Answer

A)  $\{ x \mid - 9 \leq x \leq 4 \}$ 
  
B)  $\{ x \mid - 9 < x < 4 \}$ 
  
C)  $\{ x \mid - 9 < x \leq 4 \}$
   
D)  $\{ x \mid - 9 \leq x < 4 \}$
   
A)  $\{ x \mid - 9 \leq x \leq 4 \}$ 
  
B)  $\{ x \mid - 9 < x < 4 \}$ 
  
C)  $\{ x \mid - 9 < x \leq 4 \}$
   
D)  $\{ x \mid - 9 \leq x < 4 \}$

Question 8

Find the indicated function value.
-$$f ( x ) = 3 x - 1 , g ( x ) = 2 x ^ { 2 } - 3$$
Find $( f + g ) ( 3 )$.

Accepted Answer

A)  23 
B)  17 
C)  29 
D)  24 
A)  23 
B)  17 
C)  29 
D)  24

Question 9

Decide whether the relation is a function.
-$$\{ ( - 3,6 ) , ( - 2,2 ) , ( 4,4 ) , ( 5 , - 8 ) \}$$

Accepted Answer

A)  function 
B)  not a function 
A)  function 
B)  not a function

Question 10

Find the indicated function value.
-$$\begin{array}{l}
\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ( \mathrm { x } ) \
\hline - 5 & - 6 \
- 3 & 0 \
0 & 9 \
3 & 18 \
5 & 24
\end{array}\
\text { For what value of } x \text { is } f ( x ) = 9 \text { ? }
\end{array}$$

Accepted Answer

A)  -3 
B)  -5 
C)  3 
D)  0 
A)  -3 
B)  -5 
C)  3 
D)  0

Question 11

Use the vertical line test to determine whether or not the graph is a graph of a function.
-

Accepted Answer

A)  not a function 
B)  function 
A)  not a function 
B)  function

Question 12

Use the vertical line test to determine whether or not the graph is a graph of a function.
-

Accepted Answer

A)  function 
B)  not a function 
A)  function 
B)  not a function

Question 13

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to
answer the question.  
-Between what two years is the difference in function values equal to 5%?

Accepted Answer

A)  between 1995 and 2000 
B)  between 1990 and 1995 
C)  between 1980 and 1985 
D)  between 1970 and 1975 
A)  between 1995 and 2000 
B)  between 1990 and 1995 
C)  between 1980 and 1985 
D)  between 1970 and 1975

Question 14

Express the interval in set builder notation and graph the interval on a number line.
-$$( - \infty , 6.5 )$$

Accepted Answer

A)  $\{ x \mid x \leq 6.5 \}$ 
  
B)  $\{ x \mid x \geq 6.5 \}$ 
  
C)  $\{ x \mid x  6.5 \}$ 
  
A)  $\{ x \mid x \leq 6.5 \}$ 
  
B)  $\{ x \mid x \geq 6.5 \}$ 
  
C)  $\{ x \mid x  6.5 \}$

Question 15

Decide whether the relation is a function.
-$$\{ ( 3 , - 3 ) , ( 3,3 ) , ( 6,9 ) , ( 8,8 ) , ( 10 , - 7 ) \}$$

Accepted Answer

A)  function 
B)  not a function 
A)  function 
B)  not a function

Question 16

Find the domain of the function.
-$$f ( x ) = \frac { - 2 x } { x + 3 }$$

Accepted Answer

A)  $( \infty , \infty )$ 
B)  $( \infty , 0 )$ or $( 0 , \infty )$ 
C)  $(  \infty, - 3 )$ or $( - 3 , \infty )$ 
D)  $(  \infty , - 3 )$ 
A)  $( \infty , \infty )$ 
B)  $( \infty , 0 )$ or $( 0 , \infty )$ 
C)  $(  \infty, - 3 )$ or $( - 3 , \infty )$ 
D)  $(  \infty , - 3 )$

Question 17

For the pair of functions, determine the domain of f + g.
-$$f ( x ) = 2 x ^ { 2 } + 4 , g ( x ) = 5 x ^ { 3 } - 2$$

Accepted Answer

A)  $( \infty , 0 )$ 
B)  $( \infty , 0 )$ or $( 0 , \infty )$ 
C)  $( \infty , \infty )$ 
D)  $( 0 , \infty )$ 
A)  $( \infty , 0 )$ 
B)  $( \infty , 0 )$ or $( 0 , \infty )$ 
C)  $( \infty , \infty )$ 
D)  $( 0 , \infty )$

Question 18

Express the interval in set builder notation and graph the interval on a number line.
-$$( - \infty , 4.5 \text { ] }$$

Accepted Answer

A)  $\{ x \mid x  4.5 \}$ 
  
A)  $\{ x \mid x  4.5 \}$

Question 19

Express the interval in set builder notation and graph the interval on a number line.
-

Accepted Answer

A)  domain: $( \infty , \infty )$
range: $ [0,5] $ 
B)  domain: $[ 0,5 ]$
range: $ (\infty, \infty) $ 
C)  domain: $( \infty , \infty )$
range: $ [2,5] $ 
D)  domain: $[ 2,5 ]$
range: $ (\infty, \infty) $ 
A)  domain: $( \infty , \infty )$
range: $ [0,5] $ 
B)  domain: $[ 0,5 ]$
range: $ (\infty, \infty) $ 
C)  domain: $( \infty , \infty )$
range: $ [2,5] $ 
D)  domain: $[ 2,5 ]$
range: $ (\infty, \infty) $

Question 20

Find the domain and range.
-$\{ ( - 1,3 ) , ( - 3 , - 9 ) , ( 9 , - 3 ) , ( 9 , - 1 ) \}$

Accepted Answer

A)  domain $= \{ - 1,9 , - 3 \}$; range $= \{ 3 , - 3 , - 9 , - 1 \}$ 
B)  domain $= \{ - 1,9 , - 3 , - 9 \}$; range $= \{ 3 , - 3 , - 9 , - 1 \}$ 
C)  domain $= \{ - 1,9 , - 3,19 \}$; range $= \{ 3 , - 3 , - 9 , - 1 \}$ 
D)  domain $= \{ 3 , - 3 , - 9 , - 1 \}$; range $= \{ - 1,9 , - 3 \}$ 
A)  domain $= \{ - 1,9 , - 3 \}$; range $= \{ 3 , - 3 , - 9 , - 1 \}$ 
B)  domain $= \{ - 1,9 , - 3 , - 9 \}$; range $= \{ 3 , - 3 , - 9 , - 1 \}$ 
C)  domain $= \{ - 1,9 , - 3,19 \}$; range $= \{ 3 , - 3 , - 9 , - 1 \}$ 
D)  domain $= \{ 3 , - 3 , - 9 , - 1 \}$; range $= \{ - 1,9 , - 3 \}$

Find the domain of the function. - $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 15 }$

Express the interval in set builder notation and graph the interval on a number line. -

Decide whether the relation is a function. - $\{ ( - 7 , - 8 ) , ( - 5,8 ) , ( 1,5 ) , ( 3 , - 4 ) \}$

Find the domain of the function. - $f ( x ) = - 5 x + 9$

Find the indicated function value. -Find $f ( 3 )$ when $f ( x ) = \frac { x ^ { 3 } + 6 } { x ^ { 2 } + 1 }$ .

Find the indicated function value. - f(x)=3-4,g(x)=2+4x-1 Find (f+g)(5)

Express the interval in set builder notation and graph the interval on a number line. - $( - 9,4 )$

Find the indicated function value. - $f ( x ) = 3 x - 1 , g ( x ) = 2 x ^ { 2 } - 3$ Find $( f + g ) ( 3 )$ .

Decide whether the relation is a function. - $\{ ( - 3,6 ) , ( - 2,2 ) , ( 4,4 ) , ( 5 , - 8 ) \}$

Find the indicated function value. - () -5 -6 -3 0 0 9 3 18 5 24 For what value of x is f(x)=9 ?

Use the vertical line test to determine whether or not the graph is a graph of a function. -

Use the vertical line test to determine whether or not the graph is a graph of a function. -

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to answer the question. -Between what two years is the difference in function values equal to 5%?

Express the interval in set builder notation and graph the interval on a number line. - $( - \infty , 6.5 )$ $Express the interval in set builder notation and graph the interval on a number line. - ( - \infty , 6.5 )$

Decide whether the relation is a function. - $\{ ( 3 , - 3 ) , ( 3,3 ) , ( 6,9 ) , ( 8,8 ) , ( 10 , - 7 ) \}$

Find the domain of the function. - $f ( x ) = \frac { - 2 x } { x + 3 }$

For the pair of functions, determine the domain of f + g. - $f ( x ) = 2 x ^ { 2 } + 4 , g ( x ) = 5 x ^ { 3 } - 2$

Express the interval in set builder notation and graph the interval on a number line. - $( - \infty , 4.5 \text { ] }$ $Express the interval in set builder notation and graph the interval on a number line. - ( - \infty , 4.5 \text { ] }$

Express the interval in set builder notation and graph the interval on a number line. -

Find the domain and range. - $\{ ( - 1,3 ) , ( - 3 , - 9 ) , ( 9 , - 3 ) , ( 9 , - 1 ) \}$

Variables, Real Numbers, and Mathematical Models

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables

Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

Inequalities and Problem Solving

Radicals, Radical Functions, and Rational Exponents

Filters

Exam 8: Basics of Functions

Find the domain of the function. - f(x)=x2x2+15f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 15 }f(x)=x2+15x2​

Express the interval in set builder notation and graph the interval on a number line. -

Decide whether the relation is a function. - {(−7,−8),(−5,8),(1,5),(3,−4)}\{ ( - 7 , - 8 ) , ( - 5,8 ) , ( 1,5 ) , ( 3 , - 4 ) \}{(−7,−8),(−5,8),(1,5),(3,−4)}

Find the domain of the function. - f(x)=−5x+9f ( x ) = - 5 x + 9f(x)=−5x+9

Find the indicated function value. -Find f(3)f ( 3 )f(3) when f(x)=x3+6x2+1f ( x ) = \frac { x ^ { 3 } + 6 } { x ^ { 2 } + 1 }f(x)=x2+1x3+6​ .

Find the indicated function value. - f(x)=3-4,g(x)=2+4x-1 Find (f+g)(5)

Express the interval in set builder notation and graph the interval on a number line. - (−9,4)( - 9,4 )(−9,4)

Find the indicated function value. - f(x)=3x−1,g(x)=2x2−3f ( x ) = 3 x - 1 , g ( x ) = 2 x ^ { 2 } - 3f(x)=3x−1,g(x)=2x2−3 Find (f+g)(3)( f + g ) ( 3 )(f+g)(3) .

Decide whether the relation is a function. - {(−3,6),(−2,2),(4,4),(5,−8)}\{ ( - 3,6 ) , ( - 2,2 ) , ( 4,4 ) , ( 5 , - 8 ) \}{(−3,6),(−2,2),(4,4),(5,−8)}

Find the indicated function value. - () -5 -6 -3 0 0 9 3 18 5 24 For what value of x is f(x)=9 ?

Use the vertical line test to determine whether or not the graph is a graph of a function. -

Use the vertical line test to determine whether or not the graph is a graph of a function. -

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to answer the question. -Between what two years is the difference in function values equal to 5%?

Express the interval in set builder notation and graph the interval on a number line. - (−∞,6.5)( - \infty , 6.5 )(−∞,6.5)

Decide whether the relation is a function. - {(3,−3),(3,3),(6,9),(8,8),(10,−7)}\{ ( 3 , - 3 ) , ( 3,3 ) , ( 6,9 ) , ( 8,8 ) , ( 10 , - 7 ) \}{(3,−3),(3,3),(6,9),(8,8),(10,−7)}

Find the domain of the function. - f(x)=−2xx+3f ( x ) = \frac { - 2 x } { x + 3 }f(x)=x+3−2x​

For the pair of functions, determine the domain of f + g. - f(x)=2x2+4,g(x)=5x3−2f ( x ) = 2 x ^ { 2 } + 4 , g ( x ) = 5 x ^ { 3 } - 2f(x)=2x2+4,g(x)=5x3−2

Express the interval in set builder notation and graph the interval on a number line. - (−∞,4.5 ] ( - \infty , 4.5 \text { ] }(−∞,4.5 ]

Express the interval in set builder notation and graph the interval on a number line. -

Find the domain and range. - {(−1,3),(−3,−9),(9,−3),(9,−1)}\{ ( - 1,3 ) , ( - 3 , - 9 ) , ( 9 , - 3 ) , ( 9 , - 1 ) \}{(−1,3),(−3,−9),(9,−3),(9,−1)}

Variables, Real Numbers, and Mathematical Models

Linear Equations and Inequalities in One Variable

Linear Equations in Two Variables

Systems of Linear Equations

Exponents and Polynomials

Factoring Polynomials

Rational Expressions

Inequalities and Problem Solving

Radicals, Radical Functions, and Rational Exponents

Filters

Find the domain of the function. - $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 15 }$

Decide whether the relation is a function. - $\{ ( - 7 , - 8 ) , ( - 5,8 ) , ( 1,5 ) , ( 3 , - 4 ) \}$

Find the domain of the function. - $f ( x ) = - 5 x + 9$

Find the indicated function value. -Find $f ( 3 )$ when $f ( x ) = \frac { x ^ { 3 } + 6 } { x ^ { 2 } + 1 }$ .

Express the interval in set builder notation and graph the interval on a number line. - $( - 9,4 )$

Find the indicated function value. - $f ( x ) = 3 x - 1 , g ( x ) = 2 x ^ { 2 } - 3$ Find $( f + g ) ( 3 )$ .

Decide whether the relation is a function. - $\{ ( - 3,6 ) , ( - 2,2 ) , ( 4,4 ) , ( 5 , - 8 ) \}$

Express the interval in set builder notation and graph the interval on a number line. - $( - \infty , 6.5 )$ $Express the interval in set builder notation and graph the interval on a number line. - ( - \infty , 6.5 )$

Decide whether the relation is a function. - $\{ ( 3 , - 3 ) , ( 3,3 ) , ( 6,9 ) , ( 8,8 ) , ( 10 , - 7 ) \}$

Find the domain of the function. - $f ( x ) = \frac { - 2 x } { x + 3 }$

For the pair of functions, determine the domain of f + g. - $f ( x ) = 2 x ^ { 2 } + 4 , g ( x ) = 5 x ^ { 3 } - 2$

Express the interval in set builder notation and graph the interval on a number line. - $( - \infty , 4.5 \text { ] }$ $Express the interval in set builder notation and graph the interval on a number line. - ( - \infty , 4.5 \text { ] }$

Find the domain and range. - $\{ ( - 1,3 ) , ( - 3 , - 9 ) , ( 9 , - 3 ) , ( 9 , - 1 ) \}$