Sullivan PreCalculus Section 2.4 Library of Functions; Piecewise-Defined Functions Objectives Graph the Functions in the Library of Functions Graph Piecewise-defined Functions

The following library of functions will be used throughout the text. Be able to recognize the shape of each graph and associate that shape with the given function. The Constant Function x y (0,c) The Identity Function x y (0,0)

The Square Function x y (0,0) The Cube Function x y (0,0)

The Square Root Function x y (0,0) x y (1,1) (-1,-1) The Reciprocal Function

(0,0) x y The Absolute Value Function The Cube Root Function x y

When functions are defined by more than one equation, they are called piecewise- defined functions. Example: The function f is defined as: a.) Find f (1)= 3 Find f (-1)= (-1) + 3 = 2 Find f (4)= - (4) + 3 = -1

b.) Determine the domain of f Domain: in interval notation or in set builder notation c.) Graph f x y

d.) Find the range of f from the graph found in part c. Range: in interval notation or in set builder notation x y