# How to write absolute value equations as piecewise equations

High School Statutory Authority: Algebra I, Adopted One Credit.  This graph, you can see that the function is constant over this interval, 4x. And then it jumps up in this interval for x, and then it jumps back down for this interval for x. So let me give myself some space for the three different intervals.

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Now this first interval is from, not including -9, and I have this open circle here. Not a closed in circle. So not including -9 but x being greater than -9 and all the way up to and including I could write that as -9 is less than x, less than or equal to Well we see, the value of the function is We have an open circle right over there.

The next interval is from -5 is less than x, which is less than or equal to Over that interval, the function is equal to, the function is a constant 6. It jumps up here. Sometimes people call this a step function, it steps up. It looks like stairs to some degree. If you are in two of these intervals, the intervals should give you the same values so that the function maps, from one input to the same output.

Over that interval, what is the value of our function? Well you see, the value of our function is a constant We have just constructed a piece by piece definition of this function. Actually, when you see this type of function notation, it becomes a lot clearer why function notation is useful even.

Hopefully you enjoyed that.

## David Lippman and Melonie Rasmussen

I always find these piecewise functions a lot of fun.In this section we will give an in depth look at intervals of validity as well as an answer to the existence and uniqueness question for first order differential equations.

Precalculus: An Investigation of Functions (2nd Ed) David Lippman and Melonie Rasmussen. IMPORTANT NOTE: This page contains details on the current, second edition of the grupobittia.com you are looking for the original first edition (black cover), please go here..

Precalculus: An Investigation of Functions is a free, open textbook covering a two-quarter pre-calculus . § Implementation of Texas Essential Knowledge and Skills for Mathematics, High School, Adopted (a) The provisions of §§ of this subchapter shall be .

Functions assign outputs to inputs. Some functions have simple rules, like "for every x, return x²." However, there can be other rules that are more elaborate. For example, "If xpiecewise functions*, because their rules aren't uniform, but consist of multiple pieces. A free online 2D graphing calculator (plotter), or curve calculator, that can plot piecewise, linear, quadratic, cubic, quartic, polynomial, trigonome.

In this overview, we will start with graphing straight lines, and then progress to other graphs. The only major difference, really, is in how many points you need to plot in order to draw a good graph.

Chapter Subchapter C