Evaluating Piecewise and Step Functions

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

Evaluating Piecewise Functions Steps to Evaluate Piecewise Functions 1.Look at the domain to see which equation to use 2.Plug in x-value 3.Solve! Ex. #1: Find a. g(-2) and b. g(2)

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

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

Domain and Range of Piecewise Functions Domain (x): the set of all input numbers - will not include points where the function(s) do not exist. The domain also controls which part of the piecewise function will be used over certain values of x. Range (y): the set of all outputs.

Points of Discontinuity These are the points where the function either “jumps” up or down or where the function has a “hole”. For example, in a previous example Has a point of discontinuity at x=1 The step function also has points of discontinuity at x=1, x=2 and x=3.

Axis of Symmetry The vertical line that splits the equation in half. For the equation the axis of symmetry is located at x = 1 This ‘axis of symmetry’ can be found by identifying the x- coordinate of the vertex (h,k), so the equation for the axis of symmetry would be x = h.

Maxima and Minima (aka extrema) In this function, the minimum is at y = 1 In this function, the minimum is at y = -2 Highest point on the graph Lowest point on the graph

Intervals of Increase and Decrease By looking at the graph of a piecewise function, we can also see where its slope is increasing (uphill), where its slope is decreasing (downhill) and where it is constant (straight line). We use the domain to define the ‘interval’. This function is decreasing on the interval x 1