Piecewise & Greatest Integer Functions

Objective: graph piecewise functions & solve word problems involving “step” functions.

How are piecewise graphs different than other graphs?What situations require a “step” function?

Piecewise FunctionsTwo or more functions that are

defined for aspecific DOMAIN (x).

**Remember**

> and < OPEN

CIRCLE

≥ and ≤ CLOSED

CIRCLE

Ex 1)

X Y X Y

Piecewise in the CalculatorUse the divide sign to separate the

equation & its domainLess than/greater than symbols are

under: 2nd, MATH

X Y X Y

1. Find g(5) 2. Find g(-3)

3. Find g(1) 4. Find g(-1)

Step FunctionsFunctions that “jump” to values

withoutincluding the values in between

Ex.x f(x)0

0.51

1.22

2.5

A cell phone plan charges you $5.00 if you talk under 10 minutes in a month. If you talk 10 minutes or more, but under 20 minutes in a given month they charge an additional $15.00. If you talk 20 minutes or more they charge you and additional $50.00.

A. Create a table of minutes vs. cost

B. Graph the function

C. Determine each person bill based on their minutes

Rena: 15 minutes Jenn: 20 minutes

Your favorite dog groomer charges according to your dog’s weight. 

If your dog is 15 pounds and under, the groomer charges $35.  If

your dog is between 15 and 40 pounds, she charges $40.  If your

dog is over 40 pounds, she charges $40, plus an additional $2 for

each pound.

(a)   Write a piecewise function that describes what your dog groomer charges.

(b)   Graph the function.

(c)   What would the groomer charge if your cute dog weighs 60 pounds?