EVALUATING PIECEWISE FUNCTIONS Piecewise Functions Piecewise functions defined

EVALUATING PIECEWISE 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: 1. Look at the domain to see which equation to use 2. Plug in x-value 3. Solve!

Let’s calculate f(-2). f(x) = x 2 + 1 , x 0 x– 1, x 0 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)?

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

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) =

Select Answers 3) f(-1) = -1 f(0) = 0 f(4/3)= -4 7) f(. 5) = 1 f(1) = 1 f(3)= 3 f(4)= 3 12) f(-4)= -4 f(-2)= -2 f(0)= 0 f(4)= --- 4) f(. 5)= 3. 75 f(1) = 3 f(3) = 6 f(4) = 7 8) f(0) = 1 f(2) = 3 f(4)= 5 f(5)= 5 13) f(1)= 3 f(2)= 5 f(7)= 8 f(11)= 5