Families and Piecewise Functions

Section 2.4 Date______Families and Piecewise Functions

Know the Function Families in the “BFF for Function Families” table!

The Greatest Integer Function: the largest integer less than or equal to the value of x Notation: f(x) = int(x) or f(x) = [x]

The value of the greatest integer function is the integer that is just before the value of x. Think LEFT!

Ex 1 Evaluate the following. a) int(5) b) int(4.2) c) int(⅜) d) int(-½) e) [ 2 ] f) [π]

Ex 2 Graph the following functions. a) f(x) = 2 int(x) b) g(x) = int(2x)

Piecewise-defined Function: a function that is defined differently for different parts of its domain. Pay attention to the domain description when evaluating and graphing.

3x  4 if  2  x  2  Ex 3 Evaluate the following when f (x)  5 if x  2  2 x  6 if x  2 a) f(-1) b) f(2) c) f(4) d) f(-4) Ex 4 Graph the following piecewise-defined functions. 3 if x  2 x  2, if x  3 a) f (x)   b) g(x)   2x if x  2 x 1, if x  3

x 2  2, if x  1  x  2 if  4  x  1   c) h(x)   x, if 1  x  1 d) j(x)   4 if x  1  x  2 3  4, if x  1 x 1 if x  1

Ex 5 An economy car rented in Florida from National Car Rental® on a weekly basis costs $95 per week. Extra days cost $24 per day until the day rate exceeds the weekly rate, in which case the weekly rate applies. Find the cost C of renting an economy car as a piecewise function of the number x days used, where 7 < x < 14. (Note: Any part of a day counts as a full day.)