Linear and Nonlinear Graphs

Linear vs nonlinear functions

How to identify using a graph or given a function

We covered linear equations on Wednesday.

• Linear means constant rate of change (Straight line!)

• No breaks

• No curves

Multiple Choice

Is this function linear or nonlinear?

• Linear
• Nonlinear

Multiple Choice

Is this function represented by the graph Linear or Nonlinear

• linear

• nonlinear

Multiple Choice

Is the graph pictured a linear or nonlinear function?

• Linear
• Nonlinear

Multiple Choice

Which graph(s) show nonlinear functions?

• Graph I, only
• Graph II, only
• Graph I and Graph II, only.
• Graph I, Graph II, and Graph III

What to do when not given a graph. Look at the forms. The linear fors are given below.

 $y-y_1=m\left(x-x_1\right)$  

y=mx+b
Ax+By=C

Linear given an equation.

• Both y and x have an exponent of 1 or 0 

• Remember we do not have to write an exponent of 1. IE $y^1=y$  

• x=4 would be linear, x has an exponent of 1, y has an exponent of 0

• Variables may be multiplied by constants.

• Addition/subtraction attached the other constants

Nonlinear examples

•  $y=x^2$  (exponent on x is 2)

•  $y=e^x$  (x is in the exponent)

•  $y=\log\left(x\right)$  (operation other then MDAS)

•  $y=\left|x\right|$  (operation other then MDAS)

•  $y=\frac{1}{x}$  (x in the denomiator means it exponent would be -1)

Multiple Choice

$$y=x^{2\ }+x$$  Is this function linear?

• Yes

• No

Multiple Choice

$$y-5=4x$$  Is this linear?

• Yes

• No

Multiple Select

Which equations represents y as a linear function of x? Select all that apply

• y=x³

• y=9x

• y=x

• $$y=\frac{1}{x}$$

Multiple Select

Which equations represent nonlinear functions? Select all that apply.

• y= 3x-4

• y=9x²+7x

• y=x

• y=2x³

• 2x²=y+4