# Write an absolute value equation as a piecewise function that is constant

We have an open circle right over there.

The constant pieces are observed across the adjacent intervals of the function, as they change value from one interval to the next.

Check with the vertical line test. Over that interval, what is the value of our function?

## Graphing absolute value piecewise functions

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. And then it jumps up in this interval for x, and then it jumps back down for this interval for x. Because then if you put -5 into the function, this thing would be filled in, and then the function would be defined both places and that's not cool for a function, it wouldn't be a function anymore. Over that interval, what is the value of our function? But what we're now going to explore is functions that are defined piece by piece over different intervals and functions like this you'll sometimes view them as a piecewise, or these types of function definitions they might be called a piecewise function definition. We have just constructed a piece by piece definition of this function. Now this first interval is from, not including -9, and I have this open circle here. One of the most famous step functions is the Greatest Integer Function. It's a little confusing because the value of the function is actually also the value of the lower bound on this interval right over here. Average rate of change: is constant on each straight line section ray of the graph.

I could write that as -9 is less than x, less than or equal to Hopefully you enjoyed that. The value of the function on these intervals will be n.

Actually, when you see this type of function notation, it becomes a lot clearer why function notation is useful even. You cannot draw a step function without removing your pencil from your paper.

## Absolute value piecewise functions worksheet answers

Here it's defined by this part. So that's why it's important that this isn't a -5 is less than or equal to. Because then if you put -5 into the function, this thing would be filled in, and then the function would be defined both places and that's not cool for a function, it wouldn't be a function anymore. Now let's keep going. More examples of Step Functions: NOTE: The re-posting of materials in part or whole from this site to the Internet is copyright violation and is not considered "fair use" for educators. Range: When finding the range of an absolute value function, find the vertex the turning point. Let's take a look at this graph right over here. Over that interval, what is the value of our function? The greatest integer function returns the largest integer less than or equal to x, for all real numbers x. You can't be in two of these intervals. You cannot draw a step function without removing your pencil from your paper. We have just constructed a piece by piece definition of this function. Then, let's see, our function f x is going to be equal to, there's three different intervals. This graph, you can see that the function is constant over this interval, 4x.
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