3.3-2 Step, 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 x 2, if x > -1 What value is the “stop sign” located at?

Example. Graph the following piece-wise function f(x) = 3 – x, if x < -2 5, if x ≥ -2

Assignment Page , 21, odd

Solutions