Linear Nonlinear Functions

Linear vs Non-Linear Functions

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Linear vs. Non-Linear Functions

A linear function shows a constant rate of change.

A nonlinear function does not have a constant rate of change.

From a Graph

When graphed, a linear function forms a single straight line.

When graphed, a non-linear function does NOT form a single straight line.

Multiple Choice

• This is the graph of a linear equation

• This is the graph of a non linear equation

Multiple Choice

Which graph is linear?

• Graph A

• Graph B

• Graph C

• Graph D

Multiple Choice

Is this graph linear or nonlinear?

• Linear

• Non-Linear

Multiple Choice

Is the graph pictured a linear or nonlinear function?

• Linear

• Nonlinear

From an Equation

• Can be written in the form y = mx + b (m & b are numbers)

• Can be written in the form y = mx (m is a number)

• Can be written in the form y = b (b is a number)

The equations of linear functions cannot have:

Multiple Choice

Is the equation linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• Linear

• Nonlinear

Multiple Choice

Is this function linear or nonlinear?

• Linear function

• Nonlinear function

Multiple Choice

Is this function linear or nonlinear?

$$y=\frac{x}{3}+4$$  

• Linear

• Nonlinear

Multiple Choice

Is this function linear or nonlinear?

$$y=x^2+3x\ +4$$  

• Linear

• Nonlinear

Multiple Choice

Is this function linear or nonlinear?

$$xy=7$$  

• linear

• nonlinear

Multiple Select

Is this relation linear or nonlinear?

$$x=-7$$  

• Linear

• Nonlinear

Multiple Select

Is this a linear function?

$$x=-7$$  

• Linear

• Nonlinear

Multiple Choice

Is the representation linear or non-linear? 

• Linear
• Non-Linear

Multiple Choice

Is this function linear or nonlinear?

$$y=x$$  

• Linear

• Nonlinear

Multiple Choice

Is the representation linear or non-linear? 

• Linear
• Non-Linear

Multiple Choice

Which equation(s) represent nonlinear functions?

• Equation 1, only
• Equations 1 and 3, only
• Equations 1, 2, and 3, only
• Equations 1, 2, 3, and 4

Multiple Choice

Which equations represent linear functions?

• Equations 1 and 2, only
• Equations 1 and 4, only
• Equations 2 and 3, only
• Equations 1, 3, and 4, only

From a Table

A linear function has a constant rate of change That means that the ratio of the change in y to the change in x is constant (the same).

 $ratio\ of\ \frac{\Delta y}{\Delta x}\ must\ be\ the\ same$  

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Why is this function linear?

• This is a linear function because it does not have a constant rate of change

• This is a linear function because it creates a curved line.

• This is a linear function because it have a constant rate of change.

• This is a linear function because it's y-intercept is (0,2)

Multiple Choice

Is this function linear?

• YES

• NO

Multiple Choice

Is this linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Fill in the Blanks

What is the constant rate of change of this linear function? Express your answer as an improper fraction using the backspace bar.

Multiple Choice

Which of the function(s) above are linear?

• Function I, only
• Function II, only
• Function I and Function II, only
• Function I, Function II, and Function III

Multiple Choice

Which answer choice is true?

• The table represents a linear function because there is a pattern for the x-coordinates and y-coordinates.
• The table represents a linear function because the ratio of the change in the y value and the change in the x value is constant.
• The table represents a nonlinear function because the ratio of the change in the y value and the change in the x value is not constant.
• The table does not represent a function because there is more than one output for at least one input.

Multiple Choice

Which equation represents y as a linear function of x?

• y=8x

• x=5

• y=4x²

• y=x³

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Multiple Select

Which show a linear function? Select 2.

Multiple Choice

A holiday meal costs $12.50 a person plus a delivery fee of $30.

• Linear
• Non-Linear

Multiple Choice

Ted runs 1 block, then 2 blocks, then 4 blocks, then 8 blocks.

• Linear
• Nonlinear

Multiple Select

Which of these functions are linear?

Select two answers.

• $$y\ =\ 3\ -\ x^2$$

• $$y=x$$

• $$y\ =\ x^3\ +\ 3$$