Question 1

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.

Accepted Answer

The slope is 11.00 dollars per week.Each week $11.00 is added to the cookie jar.

Question 2

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

Accepted Answer

A) True 
 B)False  False

Question 3

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? ​

Accepted Answer

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

Question 4

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

Accepted Answer

A)    
B)    
C)    
D)  ​   
A)    
B)    
C)    
D)  ​

Question 5

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

Accepted Answer

A)    
B)    
C)  ​   
D)    
A)    
B)    
C)  ​   
D)

Question 6

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.

Accepted Answer

A) True 
 B)False

Question 7

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.

Accepted Answer

A) True 
 B)False

Question 8

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.

Accepted Answer

The slope is 2.18 feet per sec

Question 9

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

Accepted Answer

A) True 
 B)False

Question 10

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

Accepted Answer

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

Question 11

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?

Accepted Answer

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. 
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 12

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.

Accepted Answer

The slope is 0.18 year per yea

Question 13

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.
​

Accepted Answer

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

Question 14

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

Accepted Answer

A) True 
 B)False

Question 15

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.

Accepted Answer

The slope is 30.00 miles per g

Question 16

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?

Accepted Answer

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

Question 17

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

Accepted Answer

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

Question 18

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.

Accepted Answer

The slope is 1.72 dollars per

Question 19

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

Accepted Answer

A)    
B)  ​   
C)    
D)    
A)    
B)  ​   
C)    
D)

Question 20

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

Accepted Answer

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 
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

Exam 12: Linear Functions

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.

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

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? ​

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

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

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.

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.

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.

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

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

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?

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.

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. ​

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

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.

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?

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

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.

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

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

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

Filters

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?

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

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

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

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?

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.

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?

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

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

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