Functions

Warm Up Figure out what the pattern is. J, F, M, A, M, J, J… S, M, T, W… O, T, T, F… George, John, Thomas, James… M, V, E, M, ... 0, 1, 1, 2, 3, 5, 8, … The most popular meal ordered at US restaurants is _________________

Figure out what the pattern is.

J, F, M, A, M, J, J…

S, M, T, W…

O, T, T, F…

George, John, Thomas, James…

M, V, E, M, ...

0, 1, 1, 2, 3, 5, 8, …

The most popular meal ordered at US restaurants is _________________

What would you pick?

What do you put in? What do you get out? How do you control what comes out?

What do you put in?

What do you get out?

How do you control what comes out?

Does the input ever change? Does the output ever change? How many items do you get out each time?

Does the input ever change?

Does the output ever change?

How many items do you get out each time?

Input Output Table On the next slide, make your own input output table for the above pattern.

On the next slide, make your own input output table for the above pattern.

Input Output Table Figure Dots 1

Let’s graph our table as if they are ordered pairs.

Let’s graph our table as if they are ordered pairs.

Graph Graph the following table. X y -2 2 -1 4 0 6 0 8 1 10 2 12

Graph the following table.

Function A function must have only one output for each input. Are the following functions? In Out 1 3 1 4 2 5 3 6 In Out 1 3 2 6 3 11 4 18 In Out 9 5 9 4 8 3 7 2

A function must have only one output for each input. Are the following functions?

Important With a function, we always want to know what we’re going to get out. If I put my dollar into the vending machine, I want my candy bar, not a bag of chips. No surprises! True of False For each input, you can have more than one output. More than one input can have the same output.

With a function, we always want to know what we’re going to get out. If I put my dollar into the vending machine, I want my candy bar, not a bag of chips. No surprises!

True of False

For each input, you can have more than one output.

More than one input can have the same output.

Vocabulary A function is a ___________ that establishes a relationship between two numbers. The collection of all the inputs is called the ______________ of a function. The collection of all the outputs is called the ______________ of a function.

A function is a ___________ that establishes a relationship between two numbers.

The collection of all the inputs is called the ______________ of a function.

The collection of all the outputs is called the ______________ of a function.