Evaluating Piecewise and Step Functions

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

Evaluating Piecewise Functions Steps: Look at the domain to see which equation to use Plug in x-value Solve! 

f(x) = x2 + 1 , x  0 x – 1 , x  0 Let’s calculate f(-2). You are being asked to output when x = -2. Since -2 is  0, you will only substitute into the first part of the function. f(-2) = (-2)2 + 1 = 5

Evaluating Piecewise Functions Which equation would we use to find; g(-5)? g(-2)? g(1)?

f(x) = 3x - 2, x  -2 -x , -2  x  1 x2 – 7x, x  1 Evaluate the following: f(-2) = ? 2 f(3) = -12 ? f(-4) = -14 ? ? f(1) = -6

Graphically, the equation would look like this: Step Functions Looks like a flight of stairs An example of a step function: Graphically, the equation would look like this:

Step Functions Evaluate: f(0.5) = f(1) = f(2) = f(3) =

Evaluate Piecewise Evaluate: f(-4) = f(-2) = f(1) = f(3) =