Piecewise & Greatest Integer Functions

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Presentation transcript:

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?

> and < OPEN CIRCLE Piecewise Functions Two or more functions that are defined for a specific DOMAIN (x). **Remember** > and < OPEN CIRCLE ≥ and ≤ CLOSED CIRCLE

Ex 1) X Y X Y

Piecewise in the Calculator Use the divide sign to separate the equation & its domain Less 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 Functions Functions that “jump” to values without including the values in between

Ex. x f(x) 0.5 1 1.2 2 2.5

A cell phone plan charges you $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. Create a table of minutes vs. cost Graph the function Determine each person bill based on their minutes Rena: 15 minutes Jenn: 20 minutes

(a) Write a piecewise function that describes what your 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?