Rate of Change Functions

Rate of Change - Linear Functions

From yesterday: constant rate function

Apple function:

• Input: number of apples, Output: price

• Could inputs be decimal numbers, ie 1.5 or 2.7?

Discrete Function

A function that includes only specific inputs, rather than all possible inputs within a range. The inputs are distinct and separate.

Examples of Discrete Functions

• Anything that cannot have partial inputs

• Buying fruit (can't buy part of an apple)

• Number of TVs in a household (can only have whole TVs)

• Number of people (cannot have partial person)

Multiple Choice

What is a discrete function?

• A function that has has only specific and distinct inputs.

• A function that has all possible inputs in a continuous range.

Which of these functions appear to be linear?

Rate of change in a linear function:

 $\frac{\text{change in y}}{\text{change in x}}=\ \frac{\text{change in output}}{\text{change in input}}$  

Multiple Choice

What fraction do we use to compute rate of change of a function?

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

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

 $\frac{\text{change in y}}{\text{change in x}}=\ \frac{\text{change in output}}{\text{change in input}}$  : rate of change will be constant in linear functions