Comparing Linear vs Nonlinear Functions

Linear versus Nonlinear Functions

Functions can be represented in graphs, tables, and equations. In this lessons you with learn how to tell when a graph, table, or equation s linear or not linear. Be sure to read each slide carefully in order to answer the questions correctly.

Linear vs. Nonlinear

• Linear functions shows a constant rate of change.

• Nonlinear functions do not have a constant rate of change.

From a Graph

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

• When graphed, a nonlinear function does not form a single straight line.

Multiple Choice

Is the function Linear or Nonlinear?

• Linear

• Nonlinear

Multiple Choice

Determine if the graph is 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

Is this graph a function or not a function? 

• Function 
• Not a Function 

From a Table

A linear function has a constant rate of change in y to the change un x is constant (the same).

Linear Functions...

have a constant rate of change. They must add or subtract by the same amount in each row. Just like this table.

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

The table represents a function. Is it linear or non-linear?

• Linear

• Nonlinear

Multiple Choice

Is the table linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Is this function linear or nonlinear?

• Linear

• Nonlinear

Multiple Choice

Linear or Nonlinear?

• Linear

• Nonlinear

Linear Functions from an equation

are represented by equations that have:

* no exponents

* no absolute value signs

* fractions with variables only in the numerator

Linear functions From an Equation

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

• Can be written in the form of y=mx (m is a number & y-intercept is the origin)

• Can be written in the form y=b (b is a number & slope is zero, not undefined)

• We will use desmos.com/calculator to determine whether an equation is linear or nonlinear

Nonlinear examples

Multiple Choice

$$y-5=4x$$  Is this linear?

• Yes

• No

Multiple Choice

Is the following linear or nonlinear?

y = x³ + 15

• Linear
• Nonlinear
• Neither

Multiple Choice

$$y=\frac{6}{x^2}\$$  

• Linear

• Nonlinear

Multiple Choice

Is the function linear or nonlinear?
y = x² + 7

• Linear
• Nonlinear

Multiple Choice

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

• Yes

• No

Multiple Choice

$$y\ =\ 6x\ +\ 5$$  

• Linear

• Nonlinear

Multiple Choice

$$y=x^4$$  

• Linear

• Nonlinear

Multiple Choice

$$\frac{x}{5}\ -^{ }65\ =y$$  

• Linear

• Nonlinear

Multiple Choice

$$\left|x\ +\ 5\right|\ =\ 43$$  

• Linear

• Nonlinear

Multiple Choice

Is the function Linear or Nonlinear?

• Linear

• Nonlinear

Multiple Choice

Is the function linear or nonlinear?

y = 2/x + 3

• Linear

• Nonlinear

Multiple Choice

LINEAR or NONLINEAR?

y = 7x³ + 5

• linear

• nonlinear

Multiple Choice

LINEAR or NONLINEAR?

y = 4x + 6

• linear

• nonlinear