2.5 Use Piecewise Functions Review: Wednesday Quiz: THURSDAY

Vocabulary A piecewise function is defined by at least two equation, each of which applies to a different part of the function’s domain. It looks like there are pieces of graphs on the coordinated plane. Points on the graph of a function in which there is a break, hole, or gap are called points of discontinuity.

Vocabulary A step function is a piecewise function that is defined by a constant value over each part of its domain. Its graph resembles a set of stairs. The average rate of change of a function between two points on its graph is the slope of the line through the two points: Average rate of change =

Example 1: Evaluate the function when x = 3

You Try: Evaluate the function when x = -4 and x = 2.

Graph: y = 3/4x – 1, if x < 4 y = -x + 3, if x > -1 y = 5x + 4, if -2 < x < 1 y = -4, if x < 5

Example 2: Graph

You Try: Graph

Example 3: Write a piecewise function for the step function shown.

Example 4: Write the function f(x) = 3|x + 1| - 2 as a piecewise function.

You Try: Write the function f(x) = |x + 4| - 1 as a piecewise function.