Question 1

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

Accepted Answer

A) True 
 B)False

Question 2

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

Accepted Answer

A) True 
 B)False

Question 3

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

Accepted Answer

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 
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 4

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

Accepted Answer

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 
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 5

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.

Accepted Answer

The slope is 0.07 do

Question 6

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?
​

Accepted Answer

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

Question 7

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.

Accepted Answer

A) True 
 B)False

Question 8

The graph of a linear function is a straight line.

Accepted Answer

A) True 
 B)False

Question 9

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.

Accepted Answer

The slope is 32 feet per secon

Question 10

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   .

Accepted Answer

A) True 
 B)False

Question 11

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? ​
​

Accepted Answer

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

Question 12

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.

Accepted Answer

A) True 
 B)False

Question 13

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?

Accepted Answer

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

Question 14

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?

Accepted Answer

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

Question 15

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

Accepted Answer

A) True 
 B)False

Question 16

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

Accepted Answer

A) True 
 B)False

Question 17

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

Accepted Answer

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 
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 18

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.

Accepted Answer

A) True 
 B)False

Question 19

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?

Accepted Answer

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

Exam 12: Linear Functions

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

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

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

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

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.

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? ​

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.

The graph of a linear function is a straight line.

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.

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 .

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? ​ ​

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.

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?

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

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

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

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.

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?

Functions Given by Formulas

Functions Given by TableChas

Functions Given by Graphs

Functions Given by Words

Table and Trends

Graphs

Solving Linear Equations

Solving Nonlinear Equations

Inequalities

Optimization

The Geometry of Lines

Modeling Data with Linear Functions

Linear Regression

Systems of Equations

Exponential Growth and Decay

Constant Percentage Change

Modeling Exponential Data

Modeling Nearly Exponential Data

Logarithmic Functions

Logistic Functions

Power Functions

Modeling Data with Power Functions

Combining and Decomposing Functions

Quadratic Functions

Higher Degree Polynomials and Rational Functions

Velocity

Rates of Change for Other Functions

Estimating Rates of Change

Equations of Change Linear and Exponential Functions

Equations of Change Graphical Solutions

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

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

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?

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?

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?

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?

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

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?