Deck 12: Linear Functions

Question 1

You can get the change in a linear function from the formula
Change in function = Slope × Change in variable.

Answer 1

True

Question 2

If a population doubles in size each day, then the population is a linear function of time with slope 2.

Answer 2

False

Question 3

The distance , in miles, I can drive without stopping for gas depends on the amount , in gallons, of fuel in the tank.The relationship is ​ .
​
If I add 5 gallons of fuel to my tank, how much farther can I drive?

A) 135.00 miles
B) 135.79 miles
C) 27.43 miles
D) 27.00 miles

Answer 3

135.00 miles

Question 4

When you order merchandise from a web site you pay shipping costs , in dollars.The shipping costs depend on the weight , in pounds, of the merchandise.The relationship is ​ ​
If my order weighs 5 pounds more than yours, how do shipping costs compare?

A) My costs are $1.87 more than yours.
B) My costs are $8.65 more than yours.
C) My costs are $8.10 more than yours.
D) My costs are $1.62 more than yours.

Question 5

The rate of change of a linear function depends on the variable of the function.

Question 6

My business pays tax on income, and the tax paid is a linear function of income.If my income is $10420 then the tax owed is $929.60.If my income is $11309 then the tax owed is $1000.72.How much tax do I owe if my income is $11874? ​

A) $1045.92
B) $1046.18
C) $949.92
D) $950.03

Question 7

You pay $10 to register at a web site.After registering you pay 59 cents for each song you download.Then the total amount you pay for music at this site is a linear function of the number of songs you download.

Question 8

You can get the rate of change of a linear function by dividing the change in the variable by the change in the function.

Question 9

If I add $5 to a cookie jar each week, then the amount of money in the cookie jar is a linear function of time with slope 5 dollars per week.

Question 10

The money I pay for music is a linear function of the number of songs I download.If I download 7 songs, then I pay $11.98.If I download 13 songs, then I pay $18.82.How much do I pay if I download 23 songs? ​
​

A) $27.16
B) $30.64
C) $26.22
D) $30.22

Question 11

A linear function is a function with a constant rate of change.

Question 12

The sales tax , in dollars, I have to pay when I buy dollars worth of merchandise is given by . ​
If I decide to buy $44 more in merchandise, how much additional sales tax will I have to pay?

A) $3.96
B) $4.76
C) $0.72
D) $0.09

Question 13

It is a fact that if you drop a rock, its velocity increases by 32 feet per second for each additional second it falls.We can conclude that the velocity of the rock is a linear function of time since the rock was dropped.

Question 14

If a rock is thrown downward with an initial velocity of 8 feet per second, then its velocity , in feet per second, after seconds is given by ​ ​
By how much does velocity increase over a 4-second period?

A) 32.16 feet per second
B) 128.09 feet per second
C) 32.00 feet per second
D) 128.00 feet per second

Question 15

If is increased by 5 units from , then is increased by 9 units.If is increased by an additional 5 units, then is increased by 11 units.We can conclude that a linear function of .

Question 16

It is a fact that if you drop a rock, it will fall 16 feet the first second of the fall.The next second it will fall 48 feet.In view of this fact, I can conclude that the distance a rock falls is a linear function of the time since the rock was dropped.

Question 17

If snow is falling at a rate of 0.5 inch each hour, then the depth of snow on the ground is a linear function of time as long as the snow continues to fall.

Question 18

The slope of the graph of a linear function is the same as the rate of change of the linear function.

Question 19

The height of a staircase is a linear function of the number of steps.

Question 20

The graph of a linear function is a straight line.

Question 21

Suppose is a linear function of .The slope is 2.44.A decrease of 7 units in causes what change in ? ​

A) A decrease of 17.08 units
B) An increase of 17.08 units
C) An increase of 2.87 units
D) A decrease of 2.87 units

Question 22

The sales tax , in dollars, I have to pay when I buy dollars worth of merchandise is given by .
Identify the slope, and explain in practical terms its meaning in terms of percentages.

Question 23

Suppose is a linear function with .If the slope of is 2.34, what is the value of ? ​

A) 23.53
B) 27.4
C) 23.4
D) 27.77

Question 24

The life expectancy , measured in years, of a child born years after 2003 is given by . ​
If one child is born 5 years after another, how much greater is the life expectancy? Assume that both children are born after 2003, so the formula above applies.
​

A) 1.51 years
B) 0.90 years
C) 5.66 years
D) 0.18 years

Question 25

Suppose is a linear function with and .Find an equation for . ​

A)
B) ​
C)
D)

Question 26

The distance , in miles, I can drive without stopping for gas depends on the amount , in gallons, of fuel in the tank.The relationship is .
Identify the slope, and explain in practical terms its meaning.

Question 27

The life expectancy , measured in years, of a child born years after 2003 is given by .
Identify the slope, and explain in practical terms what it means.

Question 28

Suppose is a linear function with and .What is the slope of ? ​

A) 0.5021568627
B) 3.47
C) 0.3921568627
D) 2.55

Question 29

Suppose is a linear function of .The slope is 2.07.An increase of 7 units in causes what change in ? ​

A) A decrease of 14.49 units
B) An increase of 14.49 units
C) An increase of 3.3816425121 units
D) A decrease of 3.3816425121 units

Question 30

When you order merchandise from a web site you pay shipping costs , in dollars.The shipping costs depend on the weight , in pounds, of the merchandise.The relationship is .
Identify the slope, and explain in practical terms its meaning.

Question 31

For a certain group of animals, the running speed , in feet per second, is a linear function of the length , in inches.The relationship is .
Identify the slope, and explain in practical terms what it means.

Question 32

Suppose is a linear function of .The slope is 2.39.A decrease of 7 units in causes what change in ? ​

A) A decrease of 16.73 units
B) An increase of 16.73 units
C) An increase of 2.9288702929 units
D) A decrease of 2.9288702929 units

Question 33

Suppose is a linear function with .If the slope of is 2.29, what value of gives ? ​

A)
B)
C)
D) ​

Question 34

I am saving money in a cookie jar.The amount of money , in dollars, in the jar after weeks is given by .
Identify the slope, and explain in practical terms what it means.

Question 35

I am saving money in a cookie jar.The amount of money , in dollars, in the jar after weeks is given by . ​
By how much do my savings grow over a 8-week period?

A) $184.29
B) $184.00
C) $23.45
D) $23.00

Question 36

Suppose is a linear function with slope 2.99.Suppose further that when .Use a formula to express as a function of . ​

A)
B)
C) ​
D)

Question 37

Suppose is a linear function of .The slope is 2.89.An increase of 7 units in causes what change in ? ​

A) A decrease of 20.23 units
B) An increase of 20.23 units
C) An increase of 2.4221453287 units
D) A decrease of 2.4221453287 units

Question 38

If a rock is thrown downward with an initial velocity of 14 feet per second, then its velocity , in feet per second, after seconds is given by .
Identify the slope, and explain in practical terms its meaning.

Question 39

For a certain group of animals, the running speed , in feet per second, is a linear function of the length , in inches.The relationship is . ​
If one animal is 5 inches longer than another, how much faster does it run?
​

A) 10.65 feet per second
B) 10.2 feet per second
C) 2.08 feet per second
D) 2.04 feet per second