Deck 2: Functions

Question 1

$A=f(s)=s^{2}$ is the area of a square of side length $s$ . What does $f(36)$ mean in terms of the square?

A) $f(36)=1296$ , the area of a square of side length 36 .
B) $f(36)=6$ , the area of a square of side length 6 .
C) $f(36)=1296$ , the area of a square of side length 1296 .
D) $f(36)=6$ , the area of a square of side length 6 .

Answer 1

$f(36)=1296$ , the area of a square of side length 36 .

Question 2

$A=f(s)=s^{2}$ is the area of a square of side length $s$ . What does $f(s)=16$ mean in terms of the square?

A) $s=256$ , the side length of a square with area 16 .
B) $s=4$ , the side length of a square with area 16 .
C) $s=16$ , the side length of a square with area 256 .
D) $s=4$ , the side length of a square with area 256 .

Answer 2

$s=4$ , the side length of a square with area 16 .

Question 3

Evaluate $f(x)=x^{2}+5 x+4$ for $x=-3$ .

Answer 3

-2

Question 4

Solve $f(x)=\sqrt{x+6}=5$ for $x$ .

Question 5

If $f(x)=\frac{1}{x+6}+5$ , find $f(-1)$ to 2 decimal places.

Question 6

If $f(x)=\frac{1}{x+5}+2$ , solve $f(x)=0$ for $x$ . Rounded to 2 decimal places.

Question 7

Suppose that your uncle Gerald has just opened a store that sells television sets. Let $P(x)$ represent the profit that he makes selling $x$ television sets per week. Suppose that he currently sells $k$ television sets per week. What is the practical interpretation of $P(2 k)$ ?

A) Twice the profit he currently makes.
B) The number of additional television sets he would have to sell per week to obtain twice the profit.
C) The profit he would make if he sold twice as many television sets per week than he currently sells.
D) Twice the number of television sets he currently sells.

Question 8

Given $g(x)=4 x^{2}-5 x$ , what is $g(5-x)$ ?

A) $-4 x^{2}+35 x-75$
B) $-4 x^{2}-35 x+75$
C) $4 x^{2}+35 x-75$
D) $4 x^{2}-35 x+75$

Question 9

For $f(x)=x^{2}-8 x+5$ , what is $f(-1)$ ?

Question 10

For $f(x)=x^{2}-4 x+5$ , what is $f(x+4)$ ?

A) $x^{2}+12 x-37$
B) $x^{2}-12 x-37$
C) $x^{2}-4 x+5$
D) $x^{2}+4 x+5$

Question 11

Let $w(m)$ give the weight (in pounds) of an average-sized baby girl who is $m$ months old. What does it mean if $w(5)=14$ ?

A) 14 baby girls weight 5 pounds.
B) 5 baby girls weight 14 pounds.
C) An average 14-month old girl weighs 5 pounds.
D) An average 5-month old girl weighs 14 pounds.

Question 12

Let $w(m)$ give the weight (in pounds) of an average-sized baby girl who is $m$ months old. What does the statement $w(p)=17$ mean?

A) The average $p$ -month old girl weighs 17 pounds.
B) The average 17-month old girl weighs $p$ pounds.
C) There are $p$ baby girls weighing 17 pounds.
D) There are 17 baby girls weighing $p$ pounds.

Question 13

Find the $y$ -coordinate of the point on the graph of $y=h(x)=\frac{1}{\sqrt{x+3}}$ whose $x$ -coordinate is 1 .

Question 14

The circumference, in $\mathrm{cm}$ , of a circle whose radius is $r \mathrm{~cm}$ is given by $C=2 \pi r$ . If $C=f(r)$ , evaluate and interpret $f(r+6)$ .

A) $2 \pi r+6$ , the circumference of a circle of radius $r+6$ .
B) $2 \pi r+6,6$ more than the circumference of a circle of radius $r$ .
C) $2 \pi r+12 \pi$ , the circumference of a circle of radius $r+6$ .
D) $2 \pi r+12,12$ more than the circumference of a circle of radius $r$ .

Question 15

The circumference, in $\mathrm{cm}$ , of a circle whose radius is $r \mathrm{~cm}$ is given by $C=2 \pi r$ . If $C=f(r)$ , evaluate and interpret $f(r)+5$ .

A) $2 \pi r+5$ , the circumference of a circle of radius $r+5$ .
B) $2 \pi r+5,5$ more than the circumference of a circle of radius $r$ .
C) $2 \pi r+10 \pi$ , the circumference of a circle of radius $r+5$ .
D) $2 \pi r+10 \pi, 5$ more than the circumference of a circle of radius $r$ .

Question 16

The data points for the following table are graphed in the figure below.

Is this the graph of a function?

Question 17

The data points for the following table are graphed in the figures below.


For the graph that is a function, we could write -----------=f(----------------), where is ------------ the dependent variable and ----------------- is the independent variable. (Fill in each blank with an $" s "$ or a " $t$ ").

Question 18

The data points for the following table are graphed in the figure below.

For the graph that is a function, approximate $f(-0.5)$ .

Question 19

The data points for the following table are graphed in the figure below.

For the graph that is a function, what is its domain?

A) $-1 \leq s \leq 6$
B) $1 \leq t \leq 5$

Question 20

Let $w(m)$ give the weight (in pounds) of an average-sized baby girl who is $m$ months old. A 16-month old baby named Amelia weighs $w(19)$ pounds. What does this tell you?

A) She is below average weight.
B) She is above average weight.
C) She is about average weight.

Question 21

Let $I(x)$ be the federal income tax paid based on a total taxable income of $x$ dollars. The value of $I(x)$ is approximated by the graph in the following figure. Which of the following would represent a decrease in your income tax if your income was $w$ dollars?

A) $I(w-300)$
B) $I(w)+1000$
C) $I(w+300)$
D) $I(w)-1000$

Question 22

Let $I(x)$ be the federal income tax paid based on a total taxable income of $x$ dollars. The value of $I(x)$ is approximated by the graph in the following figure. In this context, which of the following is greater?

A) $I(x+800)$
B) $I(x)+800$

Question 23

Assume that height is a function of age and that $H=f(a)$ is the average height (in inches) for females in the US at age $a$ years. What is the practical interpretation of $f(20)$ ?

A) The number of US females who are 20 years old.
B) The number of US females who are 20 inches tall.
C) The average height of a US female who is 20 years old.
D) The average age of a US female who is 20 inches tall.

Question 24

Assume that height is a function of age and that $H=f(a)$ is the average height (in inches) for females in the US at age $a$ years. What is the practical interpretation of $f(z)+10$ ?

A) $z$ plus the number of US females who are 10 inches tall.
B) 10 plus the number of US females who are $z$ inches tall.
C) 10 years older than the average US female who is $z$ inches tall.
D) 10 inches taller than the average height of a $z$ year old US female.

Question 25

For $f(x)=x^{2}-3 x+4$ , what is $f\left(\frac{1}{x-2}\right)$ ?

A) $\frac{4 x^{2}-19 x+23}{x^{2}-4 x+4}$
B) $\frac{4 x^{2}-19 x-9}{x^{2}-4 x+4}$
C) $\frac{4 x^{2}-13 x-9}{x^{2}-4 x+4}$
D) $\frac{4 x^{2}-13 x+11}{x^{2}-4 x+4}$

Question 26

In the following graph, is $n$ a function of $m$ ?

Question 27

A supermarket only sells cans of soda in 6-packs. The price of a 6-pack is $\$ 1.55$ . Let $C(x)$ be the total cost if you need $x$ cans of soda. What is $C(55)$ ?

Question 28

Let $f(x)=\frac{3 x+9}{2 x+1}$ . For what value of $x$ is $f(x)=3$ ?

Question 29

Let $f(x)=2 x^{2}-5$ . For what value of $x$ is $f(x)=27$ ?

Question 30

If $f(x)=-3 x-6$ , evaluate the expression $3 f(-1)-f(5)$ .

Question 31

Let $f(x)=\frac{x}{3}+3$ . Complete the table.

Question 32

What is the domain of $y=h(x)=\frac{4}{\sqrt{x+a}}$ , where $a$ is a constant?

A) $y>0$
B) $x>-a$
C) $y>4$
D) $x>a$

Question 33

Let $f(x)=\frac{2}{x+|x|}$ . What is the domain of $f(x)$ ?

A) $f(x)>2$
B) $f(x)<2$
C) $x<0$
D) $x>0$

Question 34

Assume that height is a function of age and that $H=f(a)$ is the average height (in inches) for females in the US at age $a$ years. What is a reasonable domain for $H=f(a)$ ?

A) $0 \leq a \leq 100$
B) $0 \leq H \leq 100$
C) $18 \leq a \leq 68$
D) $18 \leq H \leq 68$

Question 35

Which of the following are not in the domain of $r(x)=\frac{1}{(x+4)^{2}}+\sqrt{3-x}$ ?

A) $x=4$
B) $x=-4$
C) $x=3$
D) All numbers $x$ such that $x>3$
E) All numbers $x$ such that $x<3$

Question 36

Which of the following are not in the range of $y=\frac{6-3 x}{7+x}$ ?

A) $y=2$
B) $y=-7$
C) $y=-3$
D) All numbers $y$ such that $y>-7$
E) All numbers y such that $y<-7$

Question 37

What is the domain of the function $f(x)=\frac{10}{\sqrt{1-x^{2}}}$ ?

A)
B)
C)
D)

Question 38

What is the range of the function $y=\frac{14}{\sqrt{4-x^{2}}}$ ?

A) $y \geq 2$
B) $y \leq 2$
C) $y \geq 14$
D) $y \leq 14$
E) $y \geq 7$
F) $y \leq 7$

Question 39

The graph of $g(x)=\sqrt{25-x^{2}}$ is shown below. What is the range of $g(x)$ ?

A) $0 \leq y \leq 5$
B) $y \leq 5$
C) $y \geq 0$
D) $-5 \leq y \leq 5$

Question 40

Assuming the entire graph of $f(x)$ is shown, what is the domain of $f(x)$ ?

A) $2 \leq x \leq 6$
B) $2 \leq x \leq 10$
C) $2 \leq y \leq 6$
D) $2 \leq y \leq 10$

Question 41

Given the domain $-1 \leq x \leq 5$ , the range of $f(x)=x^{2}-1$ is --------------- $\leq y \leq$ ------------

Question 42

An organization has 175 raffle tickets to sell for $\$ 5$ each. From the proceeds of the sale, they will award the winning ticket holder $\$ 100$ . The profit, $P$ , that the organization receives is a function of the number, $n$ , of tickets sold. Assuming they sell at least one ticket, the range of this function is ------------- $\leq$ ------------ $\leq$ -----------.

Question 43

A model rocket is launched from the roof of a building. For height $h$ , in meters, and time $t$ , in seconds, after the rocket is launched, the height of the rocket above the ground is given by $h=f(t)=-4.9 t^{2}+47 t+18$ . The range of this function is approximately --------------- $\leq h \leq$ ------------ Round to the nearest whole number.

Question 44

A model rocket is launched from the roof of a building. For height $h$ , in meters, and time $t$ , in seconds, after the rocket is launched, the height of the rocket above the ground is given by $h=f(t)=-4.9 t^{2}+43 t+21$ . Interpret the domain of the graph of $f(t)$ .

A) The time it takes for the rocket to hit the ground
B) The rocket's initial height
C) The heights the rocket reaches
D) The time the rocket is in the air
E) The maximum height obtained by the rocket.

Question 45

Given the following table of values, can you conclude that $f(x)=g(x)$ ?

Question 46

A supermarket only sells cans of soda in 6-packs. The price of a 6-pack is $\$ 1.85$ . Let $C(x)$ be the total cost if you need $x$ cans of soda. What is the range of $C(x)$ ?

A) All nonnegative multiples of 6 .
B) All nonnegative multiples of 1.85 .
C) All nonnegative multiples of $1.85 * 6$ .
D) All real numbers.

Question 47

Find the domain and range of the function $f(x)=\frac{-2}{\sqrt{x-8}}$

Question 48

Find the domain of the function $h(x)=\frac{2}{x^{2}-25}$ .

Question 49

Find the domain and range of the function $h(x)=\frac{-3}{x^{2}+4}$

Question 50

Find the domain of the function $g(x)=\sqrt{\frac{3 x}{x-5}}$ .

Question 51

Let $f(x)=\frac{7}{(x-3)^{2}}$ .
a) Graph $f(x)$ .
b) Use the graph to find the range of the function on the domain $[-2,4]$ .

Question 52

Which of the following is the range of the function $P=g(x)=\left\{\begin{array}{cc}-x+6, & x \leq-2 \\ 8, & -2<x \leq 3 \\ x+5, & x>3\end{array}\right.$ ?

A) $P \geq 8$
B) $-8 \leq P \leq 8$
C) $P \geq-8$
D) all real numbers

Question 53

Evaluate $h(0)$ if $h(x)=\left\{\begin{array}{cc}3 x+6, & x \leq-2 \\ -x^{2}+4, & x>-2\end{array}\right.$

Question 54

Does the following figure show an accurate graph of $f(x)=\left\{\begin{array}{cc}1, & -2 \leq x<0 \\ x^{2}, & 0 \leq x<2 \\ x, & 2 \leq x \leq 4\end{array}\right.$ ?

Question 55

ComGas, the Cambridge power company, charges its customers $\$ 6.78$ a month, plus an additional $\$ 1.00$ per therm up to 32 therms and $\$ 0.66$ per therm above 32 therms. (A therm is a unit of gas supplied.) Let $C(x)$ be the monthly cost in dollars for using $x$ therms. Which of the following is the formula for $C$ ?

A) $C(x)=\left\{\begin{array}{lc}6.78+1.00 x, & 0 \leq x \leq 32 \\ 6.78+0.66 x, & x>32\end{array}\right.$
B) $C(x)=\left\{\begin{array}{cc}6.78+1.00 x, & 0 \leq x \leq 32 \\ 38.78+0.66 x, & x>32\end{array}\right.$
C) $C(x)=\left\{\begin{array}{cc}6.78+1.00 x, & 0 \leq x \leq 32 \\ 6.78+0.66(x-32), & x>32\end{array}\right.$
D) $C(x)=\left\{\begin{array}{cc}6.78+1.00 x, & 0 \leq x \leq 32 \\ 38.78+0.66(x-32), & x>32\end{array}\right.$

Question 56

A T-shirt printing company charges a set-up fee of $\$ 15$ for each order, plus the cost per shirt shown in the table.

Let $C$ be the total cost in dollars for printing $n$ shirts. Which of the following is the formula for $C$ ?

A)

B)

C)

D)

Question 57

Graph the function:

Question 58

Write a formula for the following function:

Question 59

Use the definition of absolute value to write a piecewise formula for $f(x)=\left|3 x^{2}-27\right|$ .

Question 60

Let Evaluate:
a) $f(-1)$
b) $f(2)$
c) $f(5)$

Question 61

Fred's cell phone company charges $\$ 60$ per month and $\$ 0.35$ for each minute (or part of a minute) over 100 minutes.
a) Write a formula for the company's policy.
b) How much is Fred's cell phone bill for the month if he talks for 138 minutes.

Question 62

Fred's cell phone company charges $\$ 60$ per month and $\$ 0.45$ for each minute (or part of a minute) over 105 minutes. Which of the following is the domain of the function?

A) $x \geq 0$
B) $x \geq 60$
C) $x \geq 105$
D) $0 \leq x \leq 105$

Question 63

Which of the following is a piecewise formula for the function $f(x)=|3 x-15|$

A) $f(x)= \begin{cases}15-3 x, & x \leq 5 \\ 3 x-15, & x>5\end{cases}$
B) $f(x)= \begin{cases}3 x-15, & x \leq 5 \\ 15-3 x, & x>5\end{cases}$
C) $f(x)= \begin{cases}15-3 x, & x \leq 15 \\ 3 x-15, & x>15\end{cases}$
D) $f(x)= \begin{cases}3 x-15, & x \leq 15 \\ 15-3 x, & x>15\end{cases}$

Question 64

Let

a) What is the domain of $f$ ?
b) What is the range of $f$ ?

Question 65

Let

a) Evaluate $f(0)$ .
b) Evaluate $f(-1)$ .
c) Evaluate $f(3)$ .

Question 66

Which of the following is a piecewise defined function for $f(x)=\frac{|2 x|}{x}$ ?

A) $f(x)= \begin{cases}-2, & x<0 \\ 2, & x>0\end{cases}$
B) $f(x)= \begin{cases}-2, & x \leq 0 \\ 2, & x>0\end{cases}$
C) $f(x)=\left\{\begin{array}{cc}-2, & x<0 \\ 0, & x=0 \\ 2, & x>0\end{array}\right.$
D) $f(x)= \begin{cases}-\frac{2}{x}, & x<0 \\ \frac{2}{x}, & x>0\end{cases}$

Question 67

Find a formula for the following graph:

Question 68

Let $f(x)= \begin{cases}2 x-5, & x \leq 0 \\ 3 x+8, & x>0\end{cases}$
a) Find the domain of $f$
b) Find the range of $f$

Question 69

Let $f(x)= \begin{cases}2 x-5, & x \leq 0 \\ 3 x+4, & x>0\end{cases}$
Graph the function.

Question 70

Let
a) Find the domain of $f$
b) Find the range of $f$

Question 71

Let
a) Evaluate $f(-5)$
b) Evaluate $f(-3)$
c) Evaluate $f(2)$
d) Evaluate $f(10)$

Question 72

Let $g(x)=\sqrt{16-x^{2}}$ . Which of the following functions will translate the graph of $g 3$ units to the left and 6 units down?

A) $h(x)=\sqrt{16-(x-3)^{2}}-6$
B) $h(x)=\sqrt{16-(x-3)^{2}}+6$
C) $h(x)=\sqrt{16-(x+3)^{2}}-6$
D) $h(x)=\sqrt{16-(x+3)^{2}}+6$

Question 73

Let $g(x)=\sqrt{25-x^{2}}$ . The range of a function that will translate the graph of $g 6$ units to the right and 2 units up is --------------- $\leq y \leq$ ------------

Question 74

The graph of $f(x)$ contains the point $(3,1)$ . What is the corresponding point on the graph of $f(x+5)$ ?

Question 75

If $r(t)=e^{t}$ for $t>0$ , what is the formula for $s(t)=r(t-4)$ ?

A) $s(t)=e^{t-4}$
B) $s(t)=e^{t}-4$
C) $s(t)=e^{t+4}$
D) $s(t)=e^{t}+4$

Question 76

If $r(t)=e^{t}$ for $t>0$ , what is the formula for $s(t)=r(t)-3$ ?

A) $s(t)=e^{t-3}$
B) $s(t)=e^{t}-3$
C) $s(t)=e^{t+3}$
D) $s(t)=e^{t}+3$

Question 77

If $f(x)=4 x^{2}+5 x$ and $g(x)=f(x-3)$ , what is $g(3)$ ?

Question 78

If $f(x)=2 x^{2}+4 x$ and $h(x)=f(x)-3$ , what is $h(-1)$ ?

Question 79

For a given function $f(x)$ , suppose $g(x)=f(x-1)$ and $h(x)=f(x)-1$ . All three functions are graphed below. Which curve shows the graph of $h$ ?

Question 80

Let $f(x)=\ln x$ and $g(x)=\ln (x+5)$ for $x>0$ . How does the graph of $g(x)$ compare to the graph of $f(x)$ ?

A) The graph of $g(x)$ is 5 units up.
B) The graph of $g(x)$ is 5 units down.
C) The graph of $g(x)$ is 5 units to the right.
D) The graph of $g(x)$ is 5 units to the left.