Deck 1: Linear Functions and Change

Question 1

Does the following graph give $y$ as a function of $x$ ?

Answer 1

True

Question 2

Use the following table to find $p(20)$ . If there is more than one answer, enter the smallest first and separate them by semicolons.

Answer 2

30

Question 3

Use the following table to find $a$ such that $p(a)=4$ . If there is more than one answer, enter the smallest first and separate them by semicolons.

Answer 3

3

Question 4

Let $y=p(x)$ be defined by the following graph. What is $p(0)$ ?

Question 5

Let $y=p(x)$ be defined by the following graph. If $p(x)=\mathrm{g}$ , what is $x$ ? If there is more than one answer, enter the smallest first and separate them by semicolons.

Question 6

Let $y=p(x)$ be defined by the following graph. Is $p(f / 2)$ closer to $g, h$ or $i$ ?

Question 7

Let $y=p(x)$ be defined by the following graph. Which of the following are true?

A)
B)
C)
D)

Question 8

Write the relationship of population, $P$ , as a function of time, $t$ , in years using function notation. Assume a direct relationship.

A) $P=f(t)$
B) $t=f(P)$
C) $t=f(1 / P)$
D) $P=f(1 / t)$

Question 9

If you were to draw a graph representing the total amount of concrete, $A$ , used to pour $x$ square feet of sidewalk, which axis would $x$ be on?

A) horizontal
B) vertical

Question 10

Consider the information in the following table.

Could $t$ be a function of $s$ ?

Question 11

You are looking at a graph of $P$ , a function of $t$ . Is it possible for the graph to intercept the $P$ -axis 5 times?

Question 12

What could the following graph reasonably represent?

A) The average daily temperature of Denver over a one-year time period with $t=0$ being July 1.
B) The average daily temperature of Denver over a one-year time period with $t=0$ being January 1.
C) The population of Denver between 1900 and 2000 with $t=0$ being 1900 .
D) The infant mortality rate in Denver between 1900 and 2000 with $t=0$ being 1900.

Question 13

Which of the following graphs is mostly likely to represent the resale price of a car which depreciates steadily until it is worthless?

A)
B)
C)
D)
E)
F)

Question 14

You have $\$ 90$ to spend on lunches this month. Each day, you can pack a lunch for about $\$ 1.75$ , or you can buy lunch at the cafeteria for $\$ 5.25$ . Let $p$ be the number of times you pack a lunch and $b$ be the number of times you buy lunch. The formula for $p$ in terms of $b$ is given by $p=$ _____ - _____ $b$ . Round answers to 2 decimal places.

Question 15

Find the value of the expression $x^{2}-3 x y$ if $x=3$ and $y=\frac{1}{5}$ .

Question 16

Solve $f(x)=0$ for $x$ using the graph of $f(x)$ below.

Question 17

Let $f(t)$ be the number of students (in thousands) attending MNO college $t$ years after 2000. Which of the following statements gives the meaning of the expression $f(15)=13$ ?

A) The number of students attending MNO college in the year 2015 is 13,000.
B) The number of students attending MNO college in the year 2000 is 13,000.
C) The number of students attending MNO college in the year 2013 is 15,000.
D) The number of students attending MNO college in the year 2000 is 15,000.

Question 18

The following chart gives the number of students in a class that are a specific height in inches

a) Is the number of students in each category a function of the height?
b) Is the height in each category a function of the number of students in that category?

Question 19

The following chart gives the number of students in a class that are a specific height in inches
a) What is the most common height of students in this class?
b) What is the least common height of students in this class?

Question 20

A box with volume $180 \mathrm{ft}^{3}$ has a square base of side length $s \mathrm{ft}$ and a height of $h \mathrm{ft}$ . Write a formula for the height of the box as a function of the side length of the box.

Question 21

Express this relationship in function notation (that is, $y$ is a function of $x$ is written $y=$ $f(x)$ ).
Calories burned, $c$ , is a function of activity, $a$ .

Question 22

The following table shows the height of a tree (to the nearest foot) as a function of time (in years). What was the average rate of change in the height of the tree between $t=6$ and $t=8$ ?

Question 23

Calculate the average rate of change for $f(x)=-x^{2}+2 x$ between $x=-3$ and $x=-2$ .

Question 24

The following figure shows the graph of $y=f(x)$ . Estimate $\Delta f(x) / \Delta x$ between $x=$ 5 and $x=10$ .

A) $\inf$
B) inf
C) $\inf$ .
D) -inf

Question 25

Is the function graphed in the following figure increasing or decreasing on the interval 5 $<\mathrm{x}<7$ ?

Question 26

If $f(x)$ is an increasing function, what can you say about $f(3)$ and $f(4)$ ?

A) $f(3)>f(4)$
B)
C) $f(3)=f(4)$
D) It cannot be determined

Question 27

Using the following figure, find the average rate of change of $f$ for $1<x<2$ .

Question 28

Let $f(x)=x^{3}$ . Find the average rate of change of the function $f$ between $x=3$ and $x=8$ .

Question 29

Let $f(x)=x^{2}$ . Find $c$ so that the average rate of change of the function $f$ between $x=1$ and $x=c$ is 8 .

Question 30

If $f(x)$ is an increasing function, which of the following must be true.

A) $f(5)>f(1)$
B) $f(5) \leq f(1)$
C) $\frac{f(1)-f(5)}{1-5}>0$
D) For some value of $x \neq 5, f(x)=f(5)$

Question 31

If $f(2)>f(3.2)$ , then the function must be a decreasing function.

Question 32

The table below gives the deer population in a state park.
$\begin{array}{lll}\text { year } & 1985 & 1990 \\ \text { number of deer } & 126 & 126\end{array}$
Using the table, find the average rate of change of the population over the interval 1990 to 2000 .

Question 33

The table below gives the deer population in a state park.

Based on the information in the chart, what would you predict about the deer population in this state park in the year 2020.

A) The deer population will be larger than 146 .
B) The deer population will be smaller than 146 .
C) The deer population will be at most 146 .

Question 34

In 2006 , you earned $\$ 8.50$ per hour at your job. In 2009 , you earned $\$ 8.70$ per hour at your job. In 2010, you earned $\$ 9.30$ per hour at your job.
a) What was the average rate of change in the amount you earned per hour between 2006 and 2009 ?
b) What was the average rate of change in the amount you earned per hour between 2009 and 2010 ?
Round answers to 3 decimal places if necessary.

Question 35

Calculate the average rate of change of the function $f(x)=8 x-3 x^{2}+12$ between $x=1$ and $x=4$ .

Question 36

If $f(x)$ is a decreasing function, which of the following is the largest:

A) $f(-8)$
B) $f(-6)$
C) $f(8)$
D) $f(1)$

Question 37

Suppose there are 110 people living in a small town and the rate of change of the town's population is 6 people per year. How many people will be living in the town twenty years from now?

Question 38

Suppose there are 100 people living in a small town and the rate of change of the town's population is 7 people per year. How many people will be living in the town twenty years from now?

A) 107
B) 140
C) 240
D) 120

Question 39

Suppose there are 150 people living in a small town and the rate of change of the town's population is -9 people per year. Which of the following must be true?

A) The town size is decreasing each year.
B) No children are born in the town each year.
C) 9 more people leave the town (move away or pass away) than join the town (move into or are born) each year.
D) No one moves into the town.

Question 40

Farmer Brown starts with 120 cows and the average rate of change of his herd is 9 cows per year. Farmer Jones starts his herd the same year with 170 cows and the average rate of change of his herd is 5 cows per year.
a) After 10 years, which farmer has the most cows?
b) After 20 years, which farmer has the most cows?

Question 41

Approximate the average rate of change for the function $f(x)$ between $x=-1$ and $x=1$

Question 42

The following table shows the relationship between $s$ , the side length of an equilateral triangle, $p$ , the perimeter of the triangle, and $A$ , the area of the triangle.

If $p$ is a linear function of $\mathrm{s}$ , give its rate of change. If it is not linear, enter "not linear".

Question 43

A salesman earns $W(n)=500+175 n$ , where $n$ is the number of products sold, and $W(n)$ is the weekly wage in dollars. What does the number 500 represent? (Mark all that apply)

A) The slope
B) The vertical intercept
C) The salesman's base salary
D) The salesman's commission for each product sold

Question 44

The distance traveled by a car is $D(t)=50 t$ miles, where $t$ is the number of hours driven. What is the slope?

Question 45

The distance traveled by a car is $D(t)=65 t$ miles, where $t$ is the number of hours driven. What is the meaning of the number 65? (Mark all that apply)

A) The vertical intercept
B) The slope
C) The total distance traveled
D) The speed of the car

Question 46

Could the following table represent a linear function?

Question 47

Could the following table represent a linear function?

Question 48

Could the following table represent a linear function?

Question 49

Which of the following figures shows the graph of a person's weight, $w$ , as a function of time $t$ , in months if the person starts out at 150 pounds and loses 5 pounds a month?

A)
B)
C)
D)

Question 50

One of the functions represented in the table below is linear. What is its vertical intercept?

Question 51

For the line $y+4=3 x-6$ ,
a) what is the slope of the line?
b) what is the y-intercept of the line?

Question 52

A cookie store has a fixed monthly cost of $\$ 540$ . It costs the cookie store $\$ 0.20$ to make a cookie and the store sells each cookie for $\$ 1.40$ . Express revenue R, cost C, and profit $\mathrm{P}$ for the cookie store when making and selling $x$ cookies in a month.

Question 53

A certain baseball card's value is given by $V=1+4.6 t$ where $t$ is the number of years after the card was issued. Interpret the constants 1 and 4.6.

Question 54

The population of a pack of rats can be represented by the formula $P(t)=3+1.3 t$ where $P(t)=3+1.3 t$ represents the population in hundreds, and $t$ represents the time, in months, since January 2010. Which of the following is correct regarding the vertical intercept?

A) Since the vertical intercept is 3, we know that in January 2010 there were 300 rats.
B) Since the vertical intercept is 3, we know that in January 2010 there were 3 rats.
C) Since the vertical intercept is 1.3 , we know that in January 2010 there were 130 rats.
D) Since the vertical intercept is 0, we know that in January 2010 there were no rats.

Question 55

The population of a pack of rats can be represented by the formula $P(t)=2+1.3 t$ where $P(t)=2+1.3 t$ represents the population in hundreds, and $t$ represents the time, in months, since January 2010. Which of the following is correct regarding the slope.

A) Since the slope is 1.3 , we know that the population is increasing by 130 rats per month.
B) Since the slope is 2, we know that the population is increasing by 200 rats per month.
C) Since the vertical intercept is 1.3 , we know that the population is increasing by approximately 1.3 rats per month.
D) Since the slope is 1.3 , we know that the population is increasing by 130 rats per year.

Question 56

A wildlife ranger finds that there is a linear relationship between the number of bushels of corn distributed in a month and the number of deer at the park. If the ranger distributes no bushels of corn, there are 49 deer at the park. For each additional bushel of corn distributed, 8 more deer come to the park.
a) If $d$ is the number of deer at the park and $b$ is the number of bushels of corn fed in a month, find a formula for $d$ in terms of $b$ .
b) How many deer are at the park if the ranger feeds 3 bushels of corn?
c) How many bushels of corn must be distributed in order to have 81 deer at the park?

Question 57

A wildlife ranger finds that there is a linear relationship between the number of bushels of corn distributed in a month and the number of deer at the park. If the ranger distributes no bushels of corn, there are 49 deer at the park. For each additional bushel of corn distributed, 7 more deer come to the park.
How many bushels of corn must be distributed in order to have 77 deer at the park?

A) 4 bushels must be distributed.
B) 588 bushels must be distributed.
C) 2 bushels must be distributed.
D) 5 bushels must be distributed.

Question 58

It costs a band $\$ 550$ to pay to rent a hall. They sell tickets for $\$ 20$ . Express the profit, $P$ , as a function of the number of people, $n$ , attending the concert.

Question 59

It costs a band $\$ 550$ to pay to rent a hall. They sell tickets for $\$ 10$ . How much profit, $P$ , will the band make if 300 people are attending the concert?

Question 60

It costs $\$ 15$ to operate a lemonade stand, while a cup of lemonade sells for $\$ 0.75$ .
Which of the following expresses the profit, $P$ , as a function of the number of cups, $c$ , of lemonade sold.

A) $P=0.75 c-15$
B) $P=0.75 c+15$
C) $P=15.75 c$
D) $P=0.75 c$

Question 61

It costs $\$ 10$ to operate a lemonade stand, while a cup of lemonade sells for $\$ 0.25$ . How many cups of lemonade must be sold in order to have $\$ 13.25$ in profit?

Question 62

What is the slope of the line $y=\frac{5}{6} x+1$ ?

Question 63

Suppose that f(x) is linear and that $f(4)=1$ and $f(0)=-7$ . If $f(x)=b+m x$ , then $b=―――$ and $m=―――$

Question 64

Suppose that $f(x)$ is linear with slope -2 and passing through the point $(5,-16)$ . If $f(x)=b+m x$ , then $b=―――$ and $m=―――$

Question 65

Suppose that $f(x)$ is linear with an $x$ -intercept of -1 and a $y$ -intercept of 5. If $f(x)=b+m x$ , then $b=―――$ and $m=―――$

Question 66

Choose the formula that represents the linear function graphed in the following figure?

A) $y=\frac{\mathrm{RT}+\mathrm{T} x}{\mathrm{R}-\mathrm{S}}$

B) $y=\frac{\mathrm{RT}-\mathrm{T} x}{\mathrm{R}-\mathrm{S}}$

C) $y=\frac{\mathrm{R}-\mathrm{T} x}{\mathrm{R}-\mathrm{S}}$

D) $y=\frac{\mathrm{T}-\mathrm{RT} x}{\mathrm{R}-\mathrm{S}}$

Question 67

If the linear equation $-3 x+4 y+1=3 x$ is written in the form $y=b+m x$ , then $b=―――$ and $m=―――$

Question 68

Let $y=b+m x$ define a linear function with slope $1 /4$ that passes through the point (-1, 3). Then $b=―――$ and $m=―――$

Question 69

Let $y=b+m x$ define a linear function with $y$ -intercept -3 that passes through the point $(-5,7)$ . Then $b=―――$ and $m=―――$

Question 70

Let $y=b+m x$ be the formula for the linear function defined in the following table.
$b=―――$ and $m=―――$

Question 71

A car company has found that there is a linear relationship between the amount of money it spends on advertising and the number of cars it sells. When it spent 50,000 dollars on advertising, it sold 425 cars. Moreover, for each additional 10 thousand dollars spent, they sell 15 more cars. Let $y=b+m x$ be the formula for the number of cars sold as a function of $x$ , the amount of money spent on advertising. Then $b=―――$ and $m=―――$

Question 72

A car company has found that there is a linear relationship between the amount of money it spends on advertising and the number of cars it sells. When it spent 60,000 dollars on advertising, it sold 680 cars. Moreover, for each additional 5 thousand dollars spent, they sell 40 more cars. Let $y=b+m x$ be the formula for the number of cars sold as a function of $x$ , the amount of money spent on advertising. What is the practical interpretation of the vertical intercept of the equation?

A) The dollars spent on advertising per car sold.
B) The number of cars sold with no money spent on advertising.
C) The amount of advertising spent before any cars are sold.
D) The number of cars sold per dollar spent on advertising.

Question 73

ComElectric, the Cambridge power company, charges its customers $\$ 9.00$ a month and $\$ 0.0675$ per kwh, plus a $\$ 0.0315$ per kwh surcharge. (A kwh, or kilowatt-hour, is a unit of electricity supplied). The formula for the monthly cost for $x$ kwh of electricity is $C=b+m x$ dollars, where $b=―――$ and $m=―――$

Question 74

If a linear population function is 50,000 in year $\mathrm{t}=0$ and grows by 1,250 people per year, then $P(t)=b+m t$ , where $b=―――$ and $m=―――$

Question 75

At a price of $\$ 2.80$ per gallon, the average weekly demand by consumers for gasoline is 43 gallons. If the price rises to $\$ 2.85$ , the weekly demand drops to 39 gallons. Assuming demand is linear, let $Q=b+m p$ , where $Q$ is the weekly quantity of gasoline demanded and $p$ is the price per gallon. Then $b=―――$ and $m=―――$

Question 76

An airplane has room for 390 coach-fare seats. It can replace any 3 coach-fare seats with 2 first-class seats. Suppose the airplane is configured with $x$ coach-fare seats and $y$ first-class seats, with no space wasted. If $x=0$ , what is the value of $y$ ?

Question 77

An airplane has room for 300 coach-fare seats. It can replace any 3 coach-fare seats with 2 first-class seats. Suppose the airplane is configured with $x$ coach-fare seats and $y$ first-class seats, with no space wasted. If $y=b+m x$ , then $b=―――$ and $m=―――$

Question 78

If a linear population function is 80,000 in year $\mathrm{t}=0$ and 87,500 by year $t=10$ , then $P(t)=b+m t$ , where $b=―――$ and $m=―――$

Question 79

An athlete wanting to strengthen his cardiovascular system will bench-press a weight, $w$ , as many times, $N$ , as possible. The following table shows the relationship between $N$ and $w$ .

Assuming this is a linear relationship, let $N=b+m w$ . Then $b=―――$ and $m=―――$

Question 80

An athlete wanting to strengthen his cardiovascular system will bench-press a weight, $w$ , as many times, $N$ , as possible. The following table shows the relationship between $N$ and $w$ .

Assuming this is a linear relationship, what is the maximum weight this athlete will be able bench-press 5 times? Round to the nearest whole number.