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!!