Linear vs 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 Blank

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

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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.

• $$y\ =\ 3\ -\ x^2$$

• $$y=x$$

• $$y\ =\ x^3\ +\ 3$$