3/5 Linear Functions

3/5 Linear Functions

Today's goals

• Identify linear functions vs. nonlinear functions

• Determine constant rate from a table or a graph

Linear functions

• NO exponents on x

• Can involve x multiplied by coefficients

• Can also involve constants

Examples of linear functions:

• The function that assigns to each number x the value 8x

• The function that assigns to each number x the value 0.5x

• The function that assigns to each number x the value 3x + 4

• The function that assigns to each number x the value  $\frac{1}{3}x$  

Examples of NON-linear functions:

• The function that assigns to each number x the value  $\sqrt{2x}$  

• The function that assigns to each number x the value  $x^2$  

• The function that assigns to each number x the value  $\frac{4}{x}$  

• The function that assigns to each number x the value  $5x^4$  

Multiple Choice

The function that assigns to each number x the value 

 $7x$  

• Linear

• Non-linear

Multiple Choice

The function that assigns to each number x the value 

 $3x+7$  

• Linear

• Non-linear

Multiple Choice

The function that assigns to each number x the value 

 $\frac{6}{x}$  

• Linear

• Non-linear

Multiple Choice

The function that assigns to each number x the value 

 $\frac{1}{3}x$  

• Linear

• Non-linear

Multiple Choice

The function that assigns to each number x the value 

 $4\sqrt{x}$  

• Linear

• Non-linear

Multiple Choice

The function that assigns to each number x the value 

 $6x^2$  

• Linear

• Non-linear

Constant rate: from a table

•  $\frac{\text{change in output}}{\text{change in input}}$  

• 
  

Constant Rate

Constant rate: from a graph

• Constant rate is the slope

•  $\frac{rise}{run}$  

Constant Rate