3.3-2Step, Piecewise, Absolute Value Functions

• Outside of linear and non-linear, we have a special set of functions whose properties do not fall into either category

• Each one is based on specific numeric properties

Greatest Integer/Step Functions

• A greatest integer function is denoted as f(x) = [|x|] – Largest integer less than or equal to x– f(3.1) = 3, f(5.9) = 5, f(0) = 0– What is f(-3.4)?

• To graph, we must identify the “jumps” in the values• Open Dots =

• Closed Dots =

Absolute Value Function

• With absolute value, we want to distance relative to 0

• Same rules as yesterday still apply• f(x) = |x|– f(-3.3) = 3.3– f(10) = 10– f(-10) = 10

• Absolute value functions have a parent function, f(x) = a|x|

• Example. Graph f(x) = -3|x|• Parent function?• What is a?

Piecewise Functions

• Piecewise = function defined in terms of two or more formulas– Come to a “stop-sign”– Stop sign then directs us which particular function

to use• Make sure you choose the correct interval

• Example. Graph the function f(x) = -2x – 2, if x ≤ -1

x2, if x > -1• What value is the “stop sign”

located at?

• Example. Graph the following piece-wise function

f(x) = 3 – x, if x < -25, if x ≥ -2

• Assignment• Page. 231• 10, 21, 25-35 odd

Solutions