Linear Functions

Functions 3

Functions

• You put a number into your machine, it does something to that number and it gives you the new number

• It does the same thing every time

• For every input, you can get only one output

• Everything we do in math is functions

You put something in, you get something out

• The function takes in a number, applies a rule to it, and spits out another number

It does the same thing every time

• The machine/function applies the same rule to every input every time, and it does it without changing the output

• Example: y = 2x

For every input, you can only get 1 output

• One input cannot have two or more different outputs

Everything we do in math is a function

• Multiplying a number by another number, raising a number to an exponent, adding two numbers are ALL functions

Open Ended

A function is:

Two inputs can have the same output

The important thing is there is only one output PER input

Friday's Exit Ticket

Linear Functions

What do you think a linear function is?

Linear Functions

A linear function is a rule described by a linear equation. The rate of change is constant, and the graph of the equation is a line.

Does this table represent a linear function? Why?

Does this table represent ALL possible inputs and outputs?

Multiple Choice

Walter walks at a constant speed of 𝟖 miles every 𝟐 hours. What is his rate of walking?

• 8 miles per hour

• 4 miles per hour

• 2 miles per hour

Open Ended

For Walter's walking function: y = 4x

x (the input) represents the number of hours he walks for.

y (the output) represents the number of miles he can walk.

What is a reasonable range of x-values for this function?

What linear function can describe this table?

Open Ended

What is an appropriate range of x-values for our running function?

 $y=\frac{1}{8}x$