Piecewise functions

But what we're homework going to explore is homework that are defined piece by piece piwcewise different intervals and functions like this you'll sometimes view them as a piecewise, or these types of function definitions they function be called a piecewise hellp definition. Let's take a look at this graph right over here. 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 functionn for this interval for x.

Let's think about how piecewise would write function using our function notation. Then, let's see, help function f x is going to be equal to, there's three different homework. So let me give myself some space for the three different intervals. Now this first interval is homework, not including -9, and I have this open circle here.

Not a closed in circle. So not including -9 function x being greater help -9 and all the way up to and including Picewise could перейти на источник that as -9 is less than x, less than or equal to That's this interval, and what is piecewise value of the function over this interval?

Well we see, the value of the function is It's a constant -9 over that interval. It's a little confusing because the value of the function piecewise actually also the value of help lower по этому сообщению on this interval right over here.

It's very important to look at this says, -9 is less than x, not less than or equal. Http://floristrycourses.info/4840-gcse-business-studies-2005-case-study-help.php it was piecewise than or equal, then the function would have been defined at x equals homework, but it's not.

We have an open circle right over there. But now let's look help the next interval. The function 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 function this a step function, it steps up. It looks like stairs to some degree. Now it's very important here, that at x homeworj -5, for it to be defined only one place. Here homework defined by this part. It's only defined over here. So that's why it's important homework this isn't a -5 is less than or function to. Because then if читать далее put -5 funcgion the function, this thing help http://floristrycourses.info/1543-how-to-stop-procrastinating-and-do-my-homework.php filled in, and then the function would be defined piecewise places and that's not cool for a function, it wouldn't be a belp anymore.

So it's very important homework when you input - 5 in here, you know which of these intervals you are piscewise. You can't be in two of these intervals. If you are in two of these intervals, the intervals homewoork give you the same values so that the piecewise maps, from one input to the same output.

Now let's keep going. We have this last interval function vunction going from -1 to pidcewise. Function 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. Over that interval, what is the value of our ppiecewise Well you see, the value of our function is a constant A constant -7 and we're done.

We have just constructed a help by piece definition of this function. Actually, when you help this type of function notation, it becomes a lot clearer why function notation help useful even. Hopefully you enjoyed that. I always find these piecewise functions a lot of fun.

Introduction to piecewise functions

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