Deck 1: Functions, Graphs, and Models; Linear Functions

Question 1

Evaluate the function.
$$\text { Given } f ( x ) = 2 x ^ { 2 } - 3 x - 3 , \text { find } f ( - 4 )$$

A) 44
B) 26
C) 1
D) 41

Answer 1

D

Question 2

Determine whether or not the relationship shown in the table is a function.
$$\begin{array} { r | r | r | r | r | r } \mathrm { x } & - 6 & - 6 & 1 & 4 & 8 \\\hline \mathrm { y } & 5 & 4 & 6 & 3 & 8\end{array}$$ Does the table define x as a function of y?

A) Yes
B) No

Answer 2

B

Question 3

Determine whether or not the relationship shown in the table is a function.
$$\begin{array} { l | c c c c } \text { Down payment (\%) } & 5 & 10 & 20 & 25 \\\hline \text { Price of Home (\$) } & 102,700 & 122,900 & 158,400 & 169,000\end{array}$$ Does the table define the price of a home that a particular family can afford as a function of the percent down payment?

A) Yes
B) No

Answer 3

A

Question 4

Determine whether or not the relationship shown in the table is a function.
$$\begin{array} { r | r | r | r | r | r } \mathrm { x } & - 2 & 2 & 4 & 9 & 10 \\\hline \mathrm { y } & 2 & 4 & - 1 & 2 & 1\end{array}$$ Does the table define y as a function of x?

A) Yes
B) No

Question 5

Determine whether or not the relationship shown in the table is a function.
$$\begin{array} { l | c c c c c c c } \text { Number of Classes Missed } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\hline \text { Average Final Exam Score } & 80 & 78 & 81 & 74 & 73 & 70 & 65\end{array}$$ Does the table define the number of classes missed as a function of the average final exam score?

A) Yes
B) No

Question 6

Determine whether or not the relationship shown in the table is a function.
$$\begin{array} { c | c } x & y \\\hline 5 & 12 \\7 & 3 \\5 & 7 \\4 & 5\end{array}$$ Does the table define y as a function of x?

A) Yes
B) No

Question 7

Determine whether or not the relationship shown in the table is a function.
$$\begin{array} { l | c c c c c c c } \text { January } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\hline \text { Weight (lbs) } & 197 & 196 & 198 & 197 & 196 & 195 & 194\end{array}$$ Does the table define weight as a function of the day in January?

A) Yes
B) No

Question 8

Use the table to answer the question.
$$\begin{array} { l | c | c | c | c | c | c | c } \mathrm { x } & - 8 & - 3 & - 1 & 0 & 1 & 9 & 15 \\\hline \mathrm { y } = \mathrm { f } ( \mathrm { x } ) & - 31 & - 16 & - 10 & - 7 & - 4 & 20 & 38\end{array}$$ Is -3 an input or output of this function?

A) Output
B) Input

Question 9

Use the table to answer the question.
$$\begin{array} { l | c | c | c | c | c | c | c } x & - 2 & 0 & 1 & 8 & 12 & 17 & 31 \\\hline y = g ( x ) & 5 & 9 & 11 & 25 & 33 & 43 & 71\end{array}$$ Is 31 an input or output of this function?

A) Input
B) Output

Question 10

For the function $y = f ( x )$ described by the table, find $f ( 2 )$ .

A) 7
B) 0
C) 2
D) Not shown

Question 11

Given $f ( x ) = x ^ { 2 } - 5 x - 1$ , find $f ( - 2 )$

A) $- 5$
B) $- 7$
C) 15
D) 13

Question 12

Determine whether or not the relationship shown in the table is a function.
$$\begin{array} { r | r } \text { Name } & \text { Test Score } \\\hline \text { Bob L. } & 80 \\\hline \text { Susan H. } & 83 \\\hline \text { Jim H. } & 76 \\\hline \text { Bruce B. } & 96\end{array}$$ Does the table define test score as a function of name?

A) Yes
B) No

Question 13

Use the table to answer the question.
$$\begin{array} { l | c | c | c | c | c | c | c } x & - 3 & 0 & 1 & 6 & 13 & 18 & 31 \\\hline y = g ( x ) & 3 & 9 & 11 & 21 & 35 & 45 & 71\end{array}$$ Is g(6) an input or output of this function?

A) Input
B) Output

Question 14

Determine whether or not the relationship shown in the table is a function.
$$\begin{array} { l | c c c c c c c } \text { January } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\hline \text { Weight (lbs) } & 218 & 217 & 219 & 218 & 217 & 216 & 215\end{array}$$ Does the table define the day in January as a function of weight?

A) Yes
B) No

Question 15

Use the table to answer the question.
$$\begin{array} { l | c | c | c | c | c | c | c } x & - 6 & - 3 & - 1 & 0 & 1 & 5 & 16 \\\hline y = f ( x ) & - 25 & - 16 & - 10 & - 7 & - 4 & 8 & 41\end{array}$$ Is f(16) an input or output of this function?

A) Input
B) Output

Question 16

Determine whether or not the relationship shown in the table is a function.
$$\begin{array} { c | c | c | c | c | c } x & 1 & 3 & 5 & 8 & 11 \\\hline y & 8 & 1 & 4 & 8 & - 3\end{array}$$ Does the table define x as a function of y?

A) Yes
B) No

Question 17

For the function $y = f ( x )$ described by the table, find $f ( 1 )$ .

A) $- 2$
B) $- 5$
C) 0
D) Not shown

Question 18

Determine whether or not the relationship shown in the table is a function.
$$\begin{array} { l | c c c c c c c } \text { Number of Classes Missed } & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\\hline \text { Average Final Exam Score } & 75 & 73 & 76 & 69 & 68 & 65 & 60\end{array}$$ Does the table define the average final exam score as a function of the number of classes missed?

A) Yes
B) No

Question 19

Evaluate the function.
Given $f ( x ) = 19 x - 4$ , find $f ( 17 )$ .

A) 19
B) 319
C) $- 327$
D) 327

Question 20

Evaluate the function.
Given $f ( x ) = ( x + 3 ) ^ { 2 }$ , find $f ( 2 )$

A) 1
B) $- 25$
C) 10
D) 25

Question 21

State whether the graph is or is not that of a function.

A) Yes
B) No

Question 22

Decide whether or not the set of ordered pairs defines a function.
$\{ ( - 6 , - 1 ) , ( - 6,7 ) , ( 2 , - 8 ) , ( 6 , - 9 ) , ( 7,2 ) \}$

A) Yes
B) No

Question 23

State whether the graph is or is not that of a function.

A) Yes
B) No

Question 24

Decide whether or not the set of ordered pairs defines a function.
$\{ ( - 3 , - 3 ) , ( - 1,5 ) , ( 4 , - 7 ) , ( 5,3 ) \}$

A) No
B) Yes

Question 25

State whether the graph is or is not that of a function.

A) Yes
B) No

Question 26

If $y = f ( x )$ , find $f ( 1 )$ .

A) 1
B) 2
C) 0
D) $- 2$

Question 27

State whether the graph is or is not that of a function.

A) Yes
B) No

Question 28

If $y = f ( x )$ , find $f ( - 2 )$ .

A) $- 1$
B) 1
C) $- 4$
D) 4

Question 29

$$\text { For the function } \mathrm { y } = \mathrm { f } ( \mathrm { x } ) \text { described by the table, find } \mathrm { f } ( 2 )$$

A) 10
B) 13
C) 7
D) 16

Question 30

Decide whether or not the set of ordered pairs defines a function.
$\{ ( - 3 , - 6 ) , ( 2 , - 8 ) , ( 6,6 ) , ( 8 , - 4 ) , ( 12 , - 1 ) \}$

A) No
B) Yes

Question 31

Decide whether or not the set of ordered pairs defines a function.
$\{ ( 2,4 ) , ( 2,7 ) , ( 4,4 ) , ( 8 , - 3 ) , ( 10,5 ) \}$

A) Yes
B) No

Question 32

State whether the graph is or is not that of a function.

A) Yes
B) No

Question 33

State whether the graph is or is not that of a function.

A) Yes
B) No

Question 34

Decide whether or not the set of ordered pairs defines a function.
$\{ ( - 6 , - 9 ) , ( - 6 , - 4 ) , ( 1,4 ) , ( 6 , - 4 ) , ( 8 , - 1 ) \}$

A) Yes
B) No

Question 35

If $y = f ( x )$ , find $f ( 4 )$ .

A) $- 2$
B) 2
C) $- 3$
D) 3

Question 36

State whether the graph is or is not that of a function.

A) Yes
B) No

Question 37

Decide whether or not the set of ordered pairs defines a function.
$\{ ( - 8 , - 8 ) , ( - 3,8 ) , ( - 2 , - 8 ) , ( 2 , - 5 ) \}$

A) Yes
B) No

Question 38

State whether the graph is or is not that of a function.

A) Yes
B) No

Question 39

Decide whether or not the set of ordered pairs defines a function.
$\{ ( - 3,5 ) , ( - 2 , - 9 ) , ( 3 , - 8 ) , ( 3,6 ) \}$

A) No
B) Yes

Question 40

Decide whether or not the set of ordered pairs defines a function.
$\{ ( - 3,8 ) , ( - 2 , - 3 ) , ( 1,3 ) , ( 1 , - 5 ) \}$

A) No
B) Yes

Question 41

Find the domain of the function.
$$y = \frac { - 8 } { x - 2 }$$

A) $( 2 , \infty )$
B) all real numbers except $- 2$
C) $( - \infty , 2 )$
D) all real numbers except 2

Question 42

Decide whether or not the arrow diagram defines a function.

A) Yes
B) No

Question 43

Decide whether or not the set of ordered pairs defines a function.
$\{ ( - 3 , - 5 ) , ( - 1,2 ) , ( 2 , - 3 ) , ( 7,2 ) \}$

A) No
B) Yes

Question 44

Find the domain of the function.
$$y = \frac { x } { \sqrt { x - 4 } }$$

A) $( 4 , \infty )$
B) all real numbers except 4
C) $[ 4 , \infty )$
D) $( - \infty , \infty )$

Question 45

Find the domain and range for the function.

A) D: $\{ - 6 , - 4 , - 2,0,2,4,6 \} ;$ R: $\{ - 4 , - 2 , - 1,3,4,6 \}$
B) D: $\{ - 6 , - 4 , - 2,2,4,6 \} ; \mathrm { R } : \{ - 4 , - 2 , - 1,3,4,6 \}$
C) D: $\{ - 6 , - 4,4,6 \} ; \mathrm { R } : \{ - 4 , - 2,4,6 \}$
D) D: $\{ - 4 , - 2 , - 1,3,4,6 \} ; \mathrm { R } : \{ - 6 , - 4 , - 2,2,4,6 \}$

Question 46

Find the domain of the function.
$$y = \sqrt { 7 + x }$$

A) $[ - 7 , \infty )$
В) $( - \infty , \infty )$
C) $( - \infty , - 7 ]$
D) $[ 0 , \infty )$

Question 47

Decide whether or not the arrow diagram defines a function.

A) No
B) Yes

Question 48

A) D: $[ 0,4 ] ; R : [ - 3,4 ]$
B) D: $[ - 3,4 ] ;$ R: $[ 0,4 ]$
C) D: $( - 3,4 ) ;$ R: $( 0,4 )$
D) D: $[ 3,4 ] ; R : [ 0,4 ]$

Question 49

Find the domain of the function.
$$y = 6 - \frac { 1 } { x }$$

A) $( - \infty , \infty )$
B) $( 6 , \infty )$
C) all real numbers except 0
D) $( - \infty , 1 )$

Question 50

Find the domain of the function.
$$y = \sqrt { 20 - x }$$

A) $( - \infty , \infty )$
B) $( \sqrt { 20 } , \infty )$
C) all real numbers except 20
D) $[ \infty , 20 ]$

Question 51

Decide whether or not the set of ordered pairs defines a function.
$\{ ( 1,4 ) , ( 2,5 ) , ( 5 , - 3 ) , ( 7,5 ) , ( 11,8 ) \}$

A) Yes
B) No

Question 52

Find the domain of the function.
$$y = \sqrt { 6 x - 5 }$$

A) $\left( \frac { 5 } { 6 } , \infty \right)$
B) $( \infty , \infty )$
C) $\left[ \frac { 5 } { 6 } , \infty \right]$
D) $\left[ - \frac { 5 } { 6 } , \infty \right)$

Question 53

Find the domain of the function.
$$y = \frac { 17 } { 12 - x }$$

A) All real numbers except 12
B) $( 12 , \infty )$
C) All real numbers except $- 12$
D) $( - \infty , 12 )$

Question 54

Decide whether or not the arrow diagram defines a function.

A) Yes
B) No

Question 55

Decide whether or not the arrow diagram defines a function.

A) No
B) Yes

Question 56

Decide whether or not the arrow diagram defines a function.

A) Yes
B) No

Question 57

A) D: $\{ - 4 , - 3,0,1,2,3 \} ;$ R: $\{ - 5 , - 2,3,5 \}$
B) D: $\{ - 5 , - 2,3,5 \} ;$ R: $\{ - 4 , - 3,1,2,3 \}$
C) D: $\{ - 4 , - 3,1,2,3 \} ;$ R: $\{ - 5 , - 2,3,5 \}$
D) D: $\{ - 5 , - 2,3,5 \} ; R : \{ - 4 , - 3,0,1,2,3 \}$

Question 58

Decide whether or not the arrow diagram defines a function.

A) No
B) Yes

Question 59

Decide whether or not the arrow diagram defines a function.

A) Yes
B) No

Question 60

A) D: $[ - 3,0 ] ;$ R: $[ - 1,3 ]$
B) D: $[ 0,3 ] ; \mathrm { R } : ( - \infty , 3 ]$
C) D: $( - \infty , 3 ] ;$ R: $[ 0,3 ]$
D) D: $[ - 1,3 ] ;$ R: $[ - 3,0 ]$

Question 61

y=10+ $\frac { 10 } { 4 x + 12 }$

A)

B) all real numbers except 3
C) $( - 3 , \infty )$
D) all real numbers except -3

Question 62

The salary s of an employee in a given year y.

A) No
B) Yes; y, s; there is one salary s in any given year y.

Question 63

Decide whether or not the equation defines y as a function of x.
$y = \frac { 6 } { x + 19 }$

A) Yes
B) No

Question 64

Suppose the cost of producing x objects was defined by the function $C ( x ) = \frac { 60 x } { \sqrt { 60 x - 10 } }$ What is the domain of the function defined by this equation?

A) $\left( \frac { 1 } { 6 } , \infty \right)$
B) $\left( \infty , \frac { 1 } { 6 } \right]$
C) $\left( x , \frac { 1 } { 6 } \right)$
D) $\left[ \frac { 1 } { 6 } , \infty \right)$

Question 65

Decide whether or not the equation defines y as a function of x.
$y = 2 x - 3$

A) Yes
B) No

Question 66

Decide whether or not the equation defines y as a function of x.
$y = 2 x ^ { 2 } + 2 x - 1$

A) Yes
B) No

Question 67

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
The balance b in a checking account on a given day x.

A) Yes; x, b; there is one balance b on a given day x.
B) No

Question 68

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
Derek's weight w in second grade g.

A) No
B) Yes; g, w; there is one weight for second grade.

Question 69

A customer's savings account number n given the number of years y the account has been active.

A) No
B) Yes; y, n; there is one account number n in any given year y.

Question 70

Decide whether or not the equation defines y as a function of x.
$y ^ { 2 } = ( x - 6 ) ( x + 4 )$

A) Yes
B) No

Question 71

Decide whether or not the equation defines y as a function of x.
$x - y ^ { 2 } = - 8$

A) Yes
B) No

Question 72

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
The temperature t on a backyard thermometer at 5 pm on a given day x.

A) Yes; x, t; there is one temperature t on any given day x at 5 pm.
B) No

Question 73

Decide whether or not the equation defines y as a function of x.
$x ^ { 2 } + y = - 6$

A) Yes
B) No

Question 74

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
Addy's height h on the first day d of school throughout elementary school.

A) No
B) Yes; d, h; there is one height for each school year.

Question 75

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
The temperature t on a backyard thermometer on a given day x.

A) Yes; x, t; there is one temperature t on any given day x.
B) No

Question 76

The number of shares s of a certain stock traded on a given day x.

A) No
B) Yes; x, s; there is one number of shares s traded on any given day x.

Question 77

This chart shows the fees for an 18-hole round of golf for each of the last 5 years at a local municipal golf course. Assume that this chart defines a function with the name of f. State the domain of f. $$\begin{array} { c | c } \text { Year } & \text { Fee } \\\hline 2008 & \$ 22 \\2009 & \$ 24 \\2010 & \$ 26 \\2011 & \$ 26 \\2012 & \$ 30\end{array}$$

A) {(2008, 22), (2009, 24), (2010, 26), (2011, 26), (2012, 30)}
B) {2008, 2009, 2010, 2011, 2012}
C) {22, 24, 26, 30}
D) {(22, 2008), (24, 2009), (26, 2010), (26, 2011), (30, 2012)}

Question 78

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
The salary s of an employee on her hiring date d.

A) No
B) Yes; d, s; there is one salary s on the hiring date d.

Question 79

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and
why the relationship is a function.
The balance in a checking account b at the close of business on a given day x.

A) Yes; x, b; there is one balance b on any given day x at the close of the business day.
B) No

Question 80

Decide whether or not the equation defines y as a function of x.
$y = \sqrt { 3 x - 7 }$

A) Yes
B) No