Piecewise Functions

Up to now, we’ve been looking at functions represented by a single equation. In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain. These are called piecewise functions.

One equation gives the value of f(x) when x ≤ 1 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 You NEVER use both X=4 X=2 X=0 This one fits Into the top equation So: 0+2=2 f(0)=2 So: 2(4) + 1 = 9 f(4) = 9 This one fits here So: 2(2) + 1 = 5 f(2) = 5 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.

Graph: Point of Discontinuity Just like the step function, we must use open and closed circles so the graph will pass the vertical line test.

Graph First graph the absolute value on the left Then, graph the quadratic on the right.