MM2A1. Students will investigate step and piecewise functions, including greatest integer and absolute value functions. b. Investigate and explain characteristics of a variety of piecewise functions including domain, range, vertex, axis of symmetry, zeros, intercepts, extrema, points of discontinuity, intervals over which the function is constant, intervals of increase and decrease, and rates of change.

Up to now, we’ve been looking at functions represented by a single equation.Up to now, we’ve been looking at functions represented by a single equation. In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain.In real life, however, functions are represented by a combination of equations, each corresponding to a part of the domain. These are calledThese are called PIECEWISE FUNCTIONS.

A piecewise function is defined by at least two equations, each of which applies to a different part of the functions domain Points on the graph of a function where there is a break, hole, or gap are called points of discontinuity

What does is mean to evaluate a piecewise function? FIRST, figure out which equation to use by checking the domainFIRST, figure out which equation to use by checking the domain NEVER use both equations NEVER use both equations THEN substitute the value for x into the equation you choseTHEN substitute the value for x into the equation you chose

Evaluate f(x) when x=0, x=2, x=4 X=0 This one fits Into the top equation So: 0+2=2 f(0)=2 X=2 This one fits here So: 2(2) + 1 = 5 f(2) = 5 X=4 This one fits here So: 2(4) + 1 = 9 f(4) = 9

Now you try! Evaluate f(x) for f(-3), f(-1), f(5)

Now you try #2! Evaluate f(x) for f(-2), f(1), f(4)

Graph: Step 1: Draw a vertical dashed line to represent the breaking point of the graph

Graph: Step 2: Substitute the domain value into the top equation to determine where to start counting the slope. (closed point or open?)

Graph: Step 3: Determine which direction you should count your slope by looking at the domain!! If x < or the value count to the LEFT of the point of discontinuity!! NOTE!!!!!!!!!!!!!! Make sure the line is sloping in the correct direction when read the function from left to right!

Graph: Step 4: Repeat Steps 2 and 3 with the bottom equation! This time, because x the domain, count the slope to the RIGHT!! NOTE!!!!!!!!!!!!!! Make sure the line is sloping in the correct direction when read the function from left to right!

x=1 is the breaking point of the graph. To the left is the top equation. To the right is the bottom equation.

Now you try to Graph: What is/are the x coordinate(s) for which there are point(s) of discontinuity???????

Now you try to Graph: What is/are the x coordinate(s) for which there are point(s) of discontinuity???????