3-1 Functions

3-1 Functions

Big Ideas Math Algebra I

Essential Question:

What is a function?

GOALS:

• Define a function

• Identify a function from a table, list of coordinate points, a diagram, and a graph

• Determine the domain and range of a function.

• Use the vertical line test.

Multiple Choice

A variable used to represent the INPUT of a function is called

• x

• y

• i

• 4

Multiple Choice

The output of a function is usually represented by..

• x

• y

What you will learn

• Determine whether relations are functions.

• Find the domain and range of a function

• Identify the independent and dependent variables of functions.

Multiple Select

In a vending machine, E6 will give you a Twix candy bar. If the vending machine IS a function, what would you expect to get the next time E6 is pressed?

• A Twix

• Snickers

• Skittles

• Hot Tamales Candy

Definitions:

Domain and Range

Domain is the set of all input (x)

Range is the set of all output (y)

Multiple Choice

A list of all of the INPUT values is called the ______ of the function.

• domain

• range

• axis

• lego

Multiple Choice

A list of all of the OUTPUT values is called the ______ of the function.

• domain

• range

• darth vader

• Marvel

Relation vs. Function (ADD to NOTES)

• A relation pairs inputs and outputs, can be ANY set of ordered pairs, (x, y)

• A function pairs each input with exactly one output.

• EXAMPLE: The vending machine that FUNCTIONS gives you skittles every time you enter E3.

• The Vertical Line Test states that any vertical line may pass through (intersect) a function no more than ONE time.

RULE of 4 (GNAW)

• Graph - Visual, coordinate plane

• Numerical: X-Y Table (input-output), Ordered Pairs, Mapping diagram, domain and range

• Algebraic - an equation, y= or f(x)

• Words - verbal or written description

Vertical Line Test

Any vertical line will pass through a FUNCTION only ONCE!

Poll

I can determine if a mapping diagram is a function or not.

• Yes

• No

• Not YET

Poll

I can determine if a set of ordered pairs is a function or not.

• Yes

• No

• Not YET

Poll

I can determine if a graph is a function or not (use the vertical line test).

• Yes

• No

• Not YET

Poll

I can identify the domain and range of a function.

• Yes

• No

• Not YET