How to write absolute value equations in piecewise formula

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.

A step function is discontinuous not continuous. This graph, you can see that the function is constant over this interval, 4x. Now it's very important here, that at x equals -5, for it to be defined only one place.

But now let's look at the next interval. 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.

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

absolute value piecewise functions worksheet answers

I always find these piecewise functions a lot of fun. Determine formulas that describe how to calculate an output from an input in each interval.

Absolute value piecewise functions worksheet answers

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. Hopefully you enjoyed that. So let me give myself some space for the three different intervals. Each formula has its own domain, and the domain of the function is the union of all these smaller domains. Now it's very important here, that at x equals -5, for it to be defined only one place. 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. This example is a function. It looks like stairs to some degree. Range: When finding the range of an absolute value function, find the vertex the turning point. All of these definitions require the output to be greater than or equal to 0. If we input 0, or a positive value, the output is the same as the input. Because 1. If it was less than or equal, then the function would have been defined at x equals -9, but it's not. So it's very important that when you input - 5 in here, you know which of these intervals you are in.

Tax brackets are another real-world example of 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. Each formula has its own domain, and the domain of the function is the union of all these smaller domains.

Absolute value piecewise functions worksheet

This example is a function. We have this last interval where we're going from -1 to 9. 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 x starts off with -1 less than x, because you have an open circle right over here and that's good because X equals -1 is defined up here, all the way to x is less than or equal to 9. If we input 0, or a positive value, the output is the same as the input. It looks like stairs to some degree. In essence, the greatest integer function rounds down a real number to the nearest integer.

If it was less than or equal, then the function would have been defined at x equals -9, but it's not. So let me give myself some space for the three different intervals.

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Absolute Value and Piecewise Functions