Piecewise Functions

Evaluating Piecewise Functions Piecewise functions are functions defined by at least two equations, each of which applies to a different part of the domain A piecewise function looks like this: Domain restrictions Equations

Steps to Evaluate Piecewise Functions Look at the domain (x-value) to see which equation to use Plug in the x-value Solve!

One equation gives the value of f(x) And the other when x > 1

Evaluate f(x) when x = 0, x = 2, x = 4 First you have to figure out which equation to use. The equations must be written so that no value of x fits more than one equation. x = 4 x = 2 x = 0 This one fits into the top equation So: 0 + 2 = 2 f(0) = 2 So: 2(2) + 1 = 5 f(2) = 5 So: 2(4) + 1 = 9 f(4) = 9 This one fits here This one fits here

Graph: For all x’s < 1, use the top graph (to the left of 1) For all x’s ≥ 1, use the bottom graph (to the right of 1)

x = 1 is the breaking point of the graph. To the left is the top equation. To the right is the bottom equation.

Point of Discontinuity Graph: Point of Discontinuity