Piecewise, Absolute Value, and Step Functions · "pieces". The constant pieces are...

Piecewise, Absolute

Value, and Step FunctionsUnit 1 - Functions

Warm – Up!!

Good Morning!! As you walk in, please pick up your

calculator and begin working on your warm-up!

1. If f(x) = 4x – 5 and g(x) = 3, find f(g(x)).

2. Find the inverse of 0 = 3x – 7.

3. What notation do we use to represent an inverse

function?

4. Define discrete and continuous. (Yes, you may google it

on your phone.)

Piecewise Functions

Example 1:

How many pieces make up this function?

Write out each piece and label what type of function it is.

Graph each piece on the appropriate domain.

Extensions: Find f(-1)= ________ f(6)= ________ f(2)= ________

Example 2:

How many pieces make up this function?

Write out each piece and label what type of function it is.

Graph each piece on the appropriate domain.

Extensions: Find f(0)= ________ f(-2)= ________ f(5)= ________

Absolute Value Functions

Example 3:Graph y=-Ix+5I.

How many pieces make up this function?

What is the domain?

What is the range?

f(3) =

f(-3) =

f(5) =

Step Functions

A step function or staircase function is a

piecewise function containing all constant

"pieces". The constant pieces are observed

across the adjacent intervals of the

function, as they change value from one

interval to the next. A step function is

discontinuous cannot draw a step function

without removing your pencil from your

paper.

Features of a Step Function

Scavenger Hunt

With a partner, you will be solving the piecewise

functions around the room by composing the piecewise

functions.

Whatever you get for your equation will take you to the

next station.

Please write down the path you follow by drawing the

sea creatures from station to station.

Once you finish, complete the practice at the end of the

guided notes.

Practice!!

Please begin working on your

practice: for each label whether it

is a piecewise, absolute value, or

step function. Then graph and find

the values asked.

Let Ms. Rhoads know if you have

any questions!!