Deck 4: Functions Functions and Function Notation

Question 1

The amount $A$ of money on deposit for $t$ years in an account earning simple interest is a linear function of $t$ . Express that function as an equation if $A = \$ 57$ when $t = 7$ and $A = \$ 27$ when $t = 1$ .
a. $A = - 5 t + 22$
b. $A = 5 t - 22$
c. $A = 27 t + 22$
d. $\quad A = 27 t - 22$
e. $\quad A = 5 t + 22$

Answer 1

E

Question 2

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 3 ) ^ { 3 }$
a.

b.

c.

d.

Answer 2

D

Question 3

Graph the function.
$$f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } - 3 x + 5 }$$
a.

b.

c.

$\mathrm { d }$ .

Answer 3

C

Question 4

Graph the function. $$y = [ [ 3 x ] ]$$
a.

b.

c.


$\mathrm { d }$ .

Question 5

A 270-room hotel is two-thirds filled when the nightly room rate is $100.Experience has shown that each $10 increase in cost results in 20 fewer occupied rooms.Find the nightly rate that will maximize
Income. a. $\$ 45.00$
b. $\$ 285.00$
c. $\$ 95.00$
d. $\$ 190.00$
e. $\$ 117.50$

Question 6

Let $f ( x ) = \sqrt { x } , g ( x ) = x + 2$ . Find the composite function which expresses the given correspondence correctly.
$\sqrt [ 4 ] { x }$
a. $\quad ( g \circ g ) ( x )$
b. $( f \circ f ) ( x )$
c. $\quad ( g \circ f ) ( x )$
d. $\quad ( f \circ g ) ( x )$
e. none of the above

Question 7

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 3 ) ^ { 3 } - 2$
a.

b.

c.


d.

Question 8

The graph of the function $f ( x )$ is a translation of the graph of $y = ( x - 1 ) ^ { 2 }$ . Graph the function. $f ( x ) = ( - x - 1 ) ^ { 2 }$
a.

b.

c.


d.

Question 9

Let $f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2$ . Find the domain of the function.
$$( f \cdot g ) ( x )$$
a. $\quad ( - \infty , 0 ]$
b. $\quad ( - \infty , 0 )$
c. $\quad ( 0 , \infty )$
d. $\quad ( - \infty , \infty )$
e. $[ 0 , \infty )$

Question 10

Evaluate the difference quotient for the function. $$f ( x ) = 3 x ^ { 2 } - 20$$
a. 3
b. $\quad 1$
c. $\quad 6$
d. $\quad 3 x + h$
e. $\quad 6 x + 3 h$

Question 11

Graph the rational function. $$f ( x ) = \frac { 5 x ^ { 3 } + 4 x } { 2 x }$$
Note that the numerator and denominator of the fraction share a common factor.
a.

b.

c.


$\mathrm { d }$ .

Question 12

Determine whether the function is one-to-one. $$y = \frac { 2 } { 5 } x$$
a. No, it isn't one-to-one.
b. Yes, it is one-to-one.

Question 13

Graph the quadratic function. $$f ( x ) = - 4 x ^ { 2 } + 2$$
a.

b.

c.

$\mathrm { d }$ .

Question 14

Let $f ( x ) = 3 x , g ( x ) = x + 1$ . Find the composite function.
$$( g \circ g ) ( x )$$
a. $\quad ( g \circ g ) ( x ) = 9 x$
b. $\quad ( g \circ g ) ( x ) = 3 x + 3$
c. $\quad ( g \circ g ) ( x ) = 3 x + 1$
d. $\quad ( g \circ g ) ( x ) = x + 2$
e. none of the above

Question 15

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 2 }$ . Graph the function. $g ( x ) = ( x + 2 ) ^ { 2 } + 3$
a.

b.

c.


d.

Question 16

A taxicab company charges $\$ 6$ for a trip up to 1 mile, and $\$ 5$ for every extra mile (or portion of a mile). Graph the ordered pairs $( m , c )$ , where $m$ represents the miles traveled and $c$ represents the cost.
a.

b.

C.


d.

Question 17

At a time $t$ seconds after an object is tossed vertically upward, it reaches a height $s$ in feet given by the equation:
$$s = 128 t - 16 t ^ { 2 }$$
In how many seconds does the object reach its maximum height?
a. $\quad 8 \mathrm { sec }$
b. $\quad 128 \mathrm { sec }$
c. $\quad 4 \mathrm { sec }$
d. $256 \mathrm { sec }$
e. $\quad 2 \mathrm { sec }$

Question 18

Find the vertex of the parabola. $$y = 2 x ^ { 2 } - 5$$
a. $\quad ( 0,2 )$
b. $\quad ( 2 , - 5 )$
c. $\quad ( - 5,2 )$
d. $\quad ( - 5,0 )$
e. $\quad ( 0 , - 5 )$

Question 19

Graph the quadratic function. $$f ( x ) = - x ^ { 2 } - 4 x + 4$$
a.

b.

c.


$\mathrm { d }$ .

Question 20

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ . Find the domain of the composite function. $( f \circ g ) ( x )$
a. $\quad ( - 1 , \infty )$
b. $\quad ( - \infty , - 1 ]$
c. $\quad ( - \infty , - 1 )$
d. $[ - 1 , \infty )$
e. $\quad ( - \infty , \infty )$

Question 21

Evaluate the difference quotient for the function. $$f ( x ) = 4 x ^ { 2 } - 14$$
a. $\quad 1$
b. $\quad 8$
c. $\quad 4 x+h$
d. $8 x+4 h$
e. 4

Question 22

The graph of the function $f ( x )$ is a translation of the graph of $y = ( x - 1 ) ^ { 10 }$ . Graph the function. $f ( x ) = ( - x - 1 ) ^ { 10 }$
a.

b.

c.


$\mathrm { d } .$

Question 23

Graph the quadratic function. $$f ( x ) = - 3 x ^ { 2 } + 2$$
a.

b.

c.


d.

Question 24

The function $f ( x ) = \sqrt { x ^ { 2 } - 6 }$ is one-to-one on the domain $x \leq - \sqrt { 6 }$ . Find $f ^ { - 1 } ( x )$ .
a. $f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } - 6 }$
b. $\quad f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 6 }$
c. $f ^ { - 1 } ( x ) = x ^ { 2 } + 6$
d. $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x ^ { 2 } - 6 } }$
e.
$$f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 6 }$$

Question 25

Find the vertex of the parabola. $$y = 2 x ^ { 2 } - 8$$
a. $\quad ( - 8,0 )$
b. $\quad ( 2 , - 8 )$
c. $\quad ( - 8,2 )$
d. $\quad ( 0 , - 8 )$
e. $\quad ( 0,2 )$

Question 26

Graph the quadratic function. $$f ( x ) = - x ^ { 2 } - 3 x + 2$$
a.

b.

c.

d.

Question 27

At a time $t$ seconds after an object is tossed vertically upward, it reaches a height $s$ in feet given by the equation:
$$s = 192 t - 16 t ^ { 2 }$$
In how many seconds does the object reach its maximum height?
a. $\quad 6 \mathrm { sec }$
b. $\quad 3 \mathrm { sec }$
c. $288 \mathrm { sec }$
d. $\quad 576 \mathrm { sec }$
e. $\quad 12 \mathrm { sec }$

Question 28

Graph the function.
$$f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x ^ { 2 } - 3 x + 5 }$$
a.

b.

c.

$\mathrm { d } .$

Question 29

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function.
a.

b.

c.


d.

Question 30

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 2 }$ . Graph the function. $g ( x ) = ( x + 4 ) ^ { 2 } + 3$
a.

b.

c.


$\mathrm { d }$ .

Question 31

Graph the rational function. $$f ( x ) = \frac { 3 x ^ { 3 } + 2 x } { 5 x }$$
Note that the numerator and denominator of the fraction share a common factor.
a.

b.

c.

d.

Question 32

Graph the function. $$y = [ [ 2 x ] ]$$
a.

b.

c.

$\mathrm { d }$

Question 33

Find the inverse of the one-to-one function. $$y = 5 x$$
a. $y = \frac { 5 } { x }$
b. $y = 25 x$
c. $y = 5 x ^ { 2 }$
d. $\quad y = \frac { x } { 5 }$
e. $\quad y = 5 x$

Question 34

Find the inverse of the one-to-one function. $$y = 3 x + 9$$
a. $\quad y = \frac { x + 9 } { 3 }$
b. $\quad y = \frac { x - 3 } { 9 }$
c. $\quad y = \frac { 3 } { x - 9 }$
d. $\quad y = \frac { x - 9 } { 3 }$
e. none of the above

Question 35

A pizzeria charges $\$ 6.00$ plus $\$ 0.65$ per topping for a large pizza. Find the cost of a pizza that has 2 toppings.
a. $\$ 4.45$
b. $\$ 8.30$
c. $\$ 4.70$
d. $\quad \$ 8.65$
e. $\$ 7.30$

Question 36

A taxicab company charges $\$ 3$ for a trip up to 1 mile, and $\$ 2$ for every extra mile (or portion of a mile). Graph the ordered pairs $( m , c )$ , where $m$ represents the miles traveled and $c$ represents the cost.
a.

b.

c.


d.

Question 37

The amount $A$ of money on deposit for $t$ years in an account earning simple interest is a linear function of $t$ . Express that function as an equation if $A = \$ 85$ when $t = 8$ and $A = \$ 40$ when $t = 3$ .
a. $A = 40 t - 13$
b. $A = 9 t + 13$
c. $A = - 9 t + 13$
d. $A = 9 t - 13$
e. $A = 40 t + 13$

Question 38

A 330-room hotel is two-thirds filled when the nightly room rate is $100.Experience has shown that each $15 increase in cost results in 30 fewer occupied rooms.Find the nightly rate that will maximize
Income. a. $\$ 105.00$
b. $\$ 315.00$
c. $\quad \$ 132.50$
d. $\$ 210.00$
e. $\$ 55.00$

Question 39

Find the range of the function $f ( x ) = \frac { 4 x } { x - 5 }$ by finding the domain of $f ^ { - 1 } ( x )$ .
a. $\quad ( - \infty , \infty )$
b. $\quad ( - \infty , 0 ) \cup ( 0 , \infty )$
c. $\quad ( - \infty , 4 ) \cup ( 4 , \infty )$
d. $\quad ( 0 , \infty )$
e. $\quad ( - \infty , 5 ) \cup ( 5 , \infty )$

Question 40

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 1 ) ^ { 3 } - 2$
a.

b.

c.

$\mathrm { d } .$

Question 41

Find the inverse of the one-to-one function. $y = 7 x$
a. $\quad y = 7 x ^ { 2 }$
b. $\quad y = 7 x$
c. $\quad y = \frac { 7 } { x }$
d. $\quad y = 49 x$
e. $y = \frac { x } { 7 }$

Question 42

Determine whether the function is one-to-one. $$y = \frac { 4 } { 7 } x$$
a. Yes, it is one-to-one.
b. No, it isn't one-to-one.

Question 43

Graph the quadratic function. $$f ( x ) = - x ^ { 2 } - 4 x + 5$$
a.

b.

c.

$\mathrm { d }$ .

Question 44

Let $f ( x ) = \sqrt { x } , g ( x ) = x + 2$ . Find the composite function which expresses the given correspondence correctly.
$\sqrt [ 4 ] { x }$
a. $\quad ( f \circ f ) ( x )$
b. $\quad ( g \circ f ) ( x )$
c. $\quad ( g \circ g ) ( x )$
d. $\quad ( f \circ g ) ( x )$
e. none of the above

Question 45

A taxicab company charges $\$ 5$ for a trip up to 1 mile, and $\$ 4$ for every extra mile (or portion of a mile). Graph the ordered pairs $( m , c )$ , where $m$ represents the miles traveled and $c$ represents the cost.
a.

b.

c.

d.

Question 46

The function $f ( x ) = \sqrt { x ^ { 2 } - 5 }$ is one-to-one on the domain $x \leq - \sqrt { 5 }$ . Find $f ^ { - 1 } ( x )$ .
a. $\quad f ^ { - 1 } ( x ) = x ^ { 2 } + 5$
b. $f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 5 }$
c. $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x ^ { 2 } - 5 } }$
d. $\quad f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 5 }$
e. $f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } - 5 }$

Question 47

Let $f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2$ . Find the domain of the function.
$$( f \cdot g ) ( x )$$
a. $\quad ( - \infty , \infty )$
b. $\quad ( - \infty , 0 ]$
c. $( - \infty , 0 )$
d. $[ 0 , \infty )$
e. $\quad ( 0 , \infty )$

Question 48

Let $f ( x ) = 3 x , g ( x ) = x + 1$ . Find the composite function.
$$( g \circ g ) ( x )$$
a. $\quad ( g \circ g ) ( x ) = 3 x + 1$
b. none of the above
c. $\quad ( g \circ g ) ( x ) = 3 x + 3$
d. $\quad ( g \circ g ) ( x ) = 9 x$
e. $\quad ( g \circ g ) ( x ) = x + 2$

Question 49

Evaluate the difference quotient for the function. $$f ( x ) = 4 x ^ { 2 } - 5$$
a. $\quad 8 x + 4 h$
b. 1
c. $\quad 8$
d. $4 x + h$
e. 4

Question 50

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 2 }$ . Graph the function. $g ( x ) = ( x + 1 ) ^ { 2 } + 3$
a.

b.

c.


d.

Question 51

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ . Find the domain of the composite function.
$$( f \circ g ) ( x )$$
a. $\quad ( - \infty , - 1 )$
b. $\quad ( - \infty , - 1 ]$
c. $\quad ( - \infty , \infty )$
d. $\quad ( - 1 , \infty )$
e. $[ - 1 , \infty )$

Question 52

Graph the function. $$y = [ [ 3 x ] ]$$
a.

b.

c.


$\mathrm { d }$ .

Question 53

Find the vertex of the parabola. $y = 3 x ^ { 2 } - 2$
a. $\quad ( - 2,0 )$
b. $\quad ( - 2,3 )$
c. $\quad ( 0,3 )$
d. $\quad ( 3 , - 2 )$
e. $\quad ( 0 , - 2 )$

Question 54

The amount $A$ of money on deposit for $t$ years in an account earning simple interest is a linear function of $t$ . Express that function as an equation if $A = \$ 28$ when $t = 1$ and $A = \$ 30$ when $t = 2$ .
a. $A = 2 t - 26$
b. $A = - 2 t + 26$
c. $\quad A = 30 t + 26$
d. $A = 2 t + 26$
e. $A = 30 t - 26$

Question 55

A 330-room hotel is two-thirds filled when the nightly room rate is $70.Experience has shown that each $5 increase in cost results in 10 fewer occupied rooms.Find the nightly rate that will maximize
Income. a. $\$ 55.00$
b. $\$ 180.00$
c. $\$ 90.00$
d. $\$ 270.00$
e. $\quad \$ 117.50$

Question 56

Find the range of the function $f ( x ) = \frac { 2 x } { x - 8 }$ by finding the domain of $f ^ { - 1 } ( x )$ .
a. $\quad ( - \infty , 0 ) \cup ( 0 , \infty )$
b. $\quad ( 0 , \infty )$
c. $( - \infty , \infty )$
d. $\quad ( - \infty , 8 ) \cup ( 8 , \infty )$
e. $\quad ( - \infty , 2 ) \cup ( 2 , \infty )$

Question 57

A pizzeria charges $\$ 12.50$ plus $\$ 0.60$ per topping for a large pizza. Find the cost of a pizza that has 3 toppings.
a. $\quad \$ 10.70$
b. $\$ 14.30$
c. $\$ 15.30$
d. $\$ 15.65$
e. $\$ 10.45$

Question 58

Graph the quadratic function. $$f ( x ) = - 3 x ^ { 2 } + 2$$
a.

b.

c.

$\mathrm { d }$ .

Question 59

Find the inverse of the one-to-one function. $$y = 2 x + 7$$
a. $y = \frac { x + 7 } { 2 }$
b. none of the above
c. $\quad y = \frac { 2 } { x - 7 }$
d. $y = \frac { x - 2 } { 7 }$
e. $y = \frac { x - 7 } { 2 }$

Question 60

At a time t seconds after an object is tossed vertically upward, it reaches a height s in feet given by the equation: $$s = 320 t - 16 t ^ { 2 }$$
In how many seconds does the object reach its maximum height?
$\begin{array} { l l } \text { a. } & 800 \mathrm { sec } \\ \text { b. } & 1,600 \mathrm { sec } \\ \text { c. } & 20 \mathrm { sec } \\ \text { d. } & 10 \mathrm { sec } \\ \text { e. } & 5 \mathrm { sec } \end{array}$

Question 61

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function. $g ( x ) = ( x - 2 ) ^ { 3 } - 5$
a.

b.

c.


d.

Question 62

Graph the function. $$f ( x ) = \frac { x ^ { 2 } - 3 x - 2 } { x ^ { 2 } - 4 x + 4 }$$
a.

b.

c.

$\mathrm { d }$ .

Question 63

The graph of the function $g ( x )$ is a translation of the graph of $f ( x ) = x ^ { 3 }$ . Graph the function.
a.

b.

c.

$\mathrm { d } .$

Question 64

Find the inverse of the one-to-one function. $$y = 3 x + 4$$
a. $y = \frac { x + 4 } { 3 }$
b. $y = \frac { x - 3 } { 4 }$
c. none of the above
d. $y = \frac { x - 4 } { 3 }$
e. $y = \frac { 3 } { x - 4 }$

Question 65

Let $f ( x ) = 2 x - 1 , g ( x ) = 3 x - 2$ . Find the domain of the function.
$$( f - g ) ( x )$$
a. $\quad ( - \infty , 0 )$
b. $\quad ( - \infty , 0 ]$
c. $( - \infty , \infty )$
d. $\quad ( 0 , \infty )$
e. $\quad [ 0 , \infty )$

Question 66

Find the inverse of the one-to-one function. $$y = 8 x$$
a. $\quad y = \frac { 8 } { x }$
b. $\quad y = \frac { x } { 8 }$
c. $\quad y = 64 x$
d. $\quad y = 8 x ^ { 2 }$
e. $y = 8 x$

Question 67

A pizzeria charges $8.50 plus $0.90 per topping for a large pizza.Find the cost of a pizza that has 5 toppings. a. $\quad \$ 13.00$
b. $\$ 3.75$
c. $\$ 14.35$
d. $\$ 4.00$
e. $\$ 14.00$

Question 68

The function $f ( x ) = \sqrt { x ^ { 2 } - 9 }$ is one-to-one on the domain $x \leq - \sqrt { 9 }$ . Find $f ^ { - 1 } ( x )$ .
a. $\quad f ^ { - 1 } ( x ) = x ^ { 2 } + 9$
b. $f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } + 9 }$
c. $f ^ { - 1 } ( x ) = \frac { 1 } { \sqrt { x ^ { 2 } - 9 } }$
d. $\quad f ^ { - 1 } ( x ) = \sqrt { x ^ { 2 } + 9 }$
e. $\quad f ^ { - 1 } ( x ) = - \sqrt { x ^ { 2 } - 9 }$

Question 69

Graph the rational function. $$f ( x ) = \frac { 2 x ^ { 3 } + 4 x } { 5 x }$$
Note that the numerator and denominator of the fraction share a common factor.
a.

b.

c.


$\mathrm { d } .$

Question 70

Find the range of the function $f ( x ) = \frac { 4 x } { x - 2 }$ by finding the domain of $f ^ { - 1 } ( x )$ .
a. $\quad ( - \infty , 2 ) \cup ( 2 , \infty )$
b. $\quad ( - \infty , 4 ) \cup ( 4 , \infty )$
c. $\quad ( - \infty , \infty )$
d. $\quad ( - \infty , 0 ) \cup ( 0 , \infty )$
e. $\quad ( 0 , \infty )$

Question 71

Determine whether the function is one-to-one. $$y = \frac { 2 } { 9 } x$$
a. No, it isn't one-to-one.
b. Yes, it is one-to-one.

Question 72

The graph of the function $f ( x )$ is a translation of the graph of $y = ( x - 1 ) ^ { 10 }$ . Graph the function. $f ( x ) = ( - x - 1 ) ^ { 10 }$
a.

b.

c.


$\mathrm { d }$ .

Question 73

Let $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 } - 1$ . Find the domain of the composite function. $( g \circ f ) ( x )$
a. $[ - 1 , \infty )$
b. $\quad ( - \infty , - 1 ]$
c. $\quad ( - \infty , - 1 )$
d. $( - \infty , \infty )$
e. $( - 1 , \infty )$

Question 74

Let $f ( x ) = \sqrt { x } , g ( x ) = x + 2$ . Find the composite function which expresses the given correspondence correctly.
$\sqrt [ 4 ] { x }$
a. $\quad ( f \circ f ) ( x )$
b. $\quad ( f \circ g ) ( x )$
c. $( g \circ f ) ( x )$
d. none of the above
e. $( g \circ g ) ( x )$

Question 75

Let $f ( x ) = 3 x , g ( x ) = x + 1$ . Find the composite function.
$$( g \circ g ) ( x )$$
a. $\quad ( g \circ g ) ( x ) = 9 x$
b. none of the above
c. $( g \circ g ) ( x ) = 3 x + 1$
d. $( g \circ g ) ( x ) = x + 2$
e. $\quad ( g \circ g ) ( x ) = 3 x + 3$