8.F.2 Compare Functions

Compare Linear and Nonlinear Functions

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It is very important for this lesson that you remember how to find the slope and the y intercept.

Let's Review

• functions are equations where any input value (often x) has only 1 output value (often y)

• You can represent a function as a graph, table or an equation

• If you have a graph you can use the vertical line test to check if it is a function

is there something you would like to go over before we continue?

Comparing Constant Rate of Change

you can compare two linear functions by comparing their constant rate of change (their slope)

The picture is an example from your book.

Linear and Non linear Functions

• a non linear function (like the function for the area of an object) does not have a constant rate of change

• a linear function will have a constant rate of change

• for these questions you will be asked if the function is linear or not.

Initial value

The other factor you can be asked to look at in the problems is the initial value. Because the initial value is going to be where the input is 0, it will be the y intercept on a graph or in an equation.

Let's try some examples

Multiple Choice

Find the rate of change

• 1

• 2

• 11

• Not a constant slope/Non-Linear

Multiple Choice

Which company shows a greater rate of change?

• Water's Edge Rafts
• Ryan's Rafts

Multiple Choice

The cost of Nate’s service is described by y = 4x + 6. The table shows the cost of Beth’s service. Which service is cheaper for 8 movies in one month?

• Beth's service ($38 vs. $40) is cheaper
• Nate’s service ($42 vs. $44) is cheaper
• Nate’s service ($38 vs. $40) is cheaper
• Beth's service ($42 vs. $44) is cheaper

Multiple Choice

Is the relation a function? Why.

• Yes, because the x-value 11 has two y-values pair with it.
• Yes, because each x-value has only one y-value paired with it.
• No, because the x-value 11 has two y-values pair with it.
• No, because each x-value has only one y-value paired with it.

Multiple Choice

Which of the following is not a function?

Multiple Choice

Is the equation linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is the graph pictured a linear or nonlinear function?

• Linear
• Nonlinear

Multiple Choice

Is this function linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Which function has the GREATEST rate of change?

Multiple Choice

What is the rate of change in the equation?
y=8x+6

• 8
• 6

Multiple Choice

What is the initial value in this equation?
y=8x+6

• 8
• 6

Multiple Choice

Find the rate of change

• 1

• 2

• 11

• Not a constant slope/Non-Linear

Multiple Choice

Find the rate of change

• 3
• -3
• 20
• Not a constant slope/Non-Linear

Multiple Choice

What is the initial value in this equation?
y=8x+6

• 8
• 6

Multiple Choice

What is the rate of change in the equation?
y=8x+6

• 8
• 6

Multiple Choice

Tim bought a new phone.  He paid $125 on the day of purchase, then $50 per month until it was paid off. What is the initial value in this situation?

• 50
• 125

Multiple Choice

Tim bought a new phone.  He paid $125 on the day of purchase, then $50 per month until it was paid off. What is the rate of change in this situation?

• 50
• 125

Multiple Choice

Which function has the GREATEST rate of change?

Multiple Choice

Which function has the GREATEST initial value?

Multiple Choice

What is a possible scenario for the given table?

• You have $8 and get $5 more each day!

• You have $16 and get $2 more each day!

• You have $2 and get $6 more each day!

• You have $6 and get $2 more each day!

Multiple Choice

Choose the correct table. You have $30 and each day you spend $3.50 on lunch.

Multiple Choice

What has the GREATER rate of change. y = 5x +15 OR the graph

• y = 5x + 15

Multiple Choice

What has the GREATER rate of change.

• y = 7x + 10

• Someone who starts with $6 and gets $8 each day.

• y = 5x + 20

• Someone who starts with $8 and gets $6 each day.

Multiple Choice

What has the greater rate of change?

• y = 19x +39

Multiple Choice

What is the greater rate of change.

• If you start with 60 points and get 1 point per assignment.

• y = 1x + 50

• They're all the same!

Multiple Choice

What is the greater initial value?

• If you start with 60 points and get 1 point per assignment.

• y = 1x + 50

• They're all the same!