# Write a definition for a piecewise function

### How to write a piecewise function from a function

I could write that as -9 is less than x, less than or equal to It's very important to look at this says, -9 is less than x, not less than or equal. Tax brackets are another real-world example of piecewise functions. It's a constant -9 over that interval. So it's very important that when you input - 5 in here, you know which of these intervals you are in. We have an open circle right over there. 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. You can't be in two of these intervals.

Show Solution To find the cost of using 1. Then, let's see, our function f x is going to be equal to, there's three different intervals.

## Piecewise linear function

Try It Graph the following piecewise function. I always find these piecewise functions a lot of fun. It looks like stairs to some degree. Now this first interval is from, not including -9, and I have this open circle here. Tax brackets are another real-world example of piecewise functions. A piecewise function is a function in which more than one formula is used to define the output over different pieces of the domain. Over that interval, what is the value of our function? We have an open circle right over there. 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. We have just constructed a piece by piece definition of this function.

It looks like stairs to some degree. It's a constant -9 over that interval. All of these definitions require the output to be greater than or equal to 0.

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. 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.

## Graphing piecewise functions examples

Over that interval, the function is equal to, the function is a constant 6. If it was less than or equal, then the function would have been defined at x equals -9, but it's not. Now let's keep going. For each piece of the domain, graph on that interval using the corresponding equation pertaining to that piece. Graph piecewise-defined functions. Use braces and if-statements to write the function. This graph, you can see that the function is constant over this interval, 4x. Well you see, the value of our function is a constant 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. It jumps up here. With a domain of all real numbers and a range of values greater than or equal to 0, absolute value can be defined as the magnitude, or modulus, of a real number value regardless of sign. I always find these piecewise functions a lot of fun. We plot the graphs for the different formulas on a common set of axes, making sure each formula is applied on its proper domain. Then, let's see, our function f x is going to be equal to, there's three different intervals. Do not graph two functions over one interval because it would violate the criteria of a function.

Now this first interval is from, not including -9, and I have this open circle here.

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