4 PIECEWISE FUNCTIONS What You Should Learn I

#4 PIECEWISE FUNCTIONS

What You Should Learn: ① I can graph any piecewise function. ① I can evaluate piecewise functions from multiple representations. ① I can distinguish between inclusive and exclusive points. ① I can write a piecewise function from multiple representations.

Graphing & Evaluating Piecewise Functions – Day 1 Today’s objective: ①I can graph any piecewise function. ①I can evaluate piecewise functions from multiple representations. ①I can distinguish between inclusive and exclusive points.

Definition of Piecewise • Root word is Piece.

Piecewise Functions: Graphically • Piecewise Functions are Pieces of different functions graphed together on the same coordinate plane. • Each of these Pieces is defined on a different domain. (x intervals) • Graphs are not continuous.

Examples of Piecewise Functions: Graphically

Piecewise Functions: Algebraically • When functions are defined by more than one equation, they are called piece-wise defined functions. • Each equation is a different Piece.

Examples of Piecewise Functions: Graphically

For the following function a) Find f(-1), f(3). b) Find the domain. c) Sketch the graph.

For the following function a) f(-1) = -1 + 3 = 2 f(1) = 3 f(3) = -3 + 3 = 0.

b) Find the domain. -2 -1 0 1 Domain of f(x): [-2, ∞)

c) Graph

c) Graph

Example 2: Graph

Example 3: Graph