1.5 I understand Functions

Function For each input there is only one output Ex: Let g represent the age of a US citizen and d represent the number of days since his or her birth. Is g a function of d or is d a function of g?

If y is a function of x

Relation A set of ordered pairs Can be indicated by a verbal description, a graph, a formula or equation, or a table Not every relation is a function, but every function is a relation.

Determine if each relation is a function: XY XY

Vertical Line Test A graph is a function if and only if there is no vertical line that crosses the graph more than once AKA: When you draw a vertical line on the graph, if it intersects with the graph more than once, it is NOT a function

Use the Vertical Line Test to determine if the graph is a function

Identifying a function from an equation

Domain and Range

Determine the Domain and Range (Put into calculators if needed)

Function Notation

Using Function Notation

Using Function Notation with Variables

The Average Rate of Change Slope = It is not necessary to have a formula for a function to find the average rate of change, you can find the average rate of change (slope) if you know two points on the graph.

Average Rate of Change (slope) Find the average rate of change between the two points.

Example 1 The population of California was 29.8 million in 1990 and 33.9 million in What was the average rate of change of the population over that time interval? Use the coordiantes (year, population) (1990, 29,800,000) and (2000, 33,900,000)

The Difference Quotient

Find and simplify the difference quotient

Find and simplify the difference quotient

Find and simplify the difference quotient

1.6 Graphs of Relations and Functions Parent Functions Graph the following parent functions and state the domain and range.

XY

XY

XY The Absolute Value Function

The square root function: XY

The Cubic function: XY

XY

XY

XY

XY