# Writing and graphing piecewise functions calculator

### How to graph piecewise functions step by step

So that's why it's important that this isn't a -5 is less than or equal to. And then I'm gonna draw the line. Well, let's see if we can graph it. This is negative 66 over 11, is that right? This is going to be, what is this? Well you see, the value of our function is a constant Now, we might be tempted, we might be tempted, to just circle in this dot over here, but remember, this interval does not include negative two. Let me do it over here where I do the, so we're going to have negative 0. I just multiplied this times 10, 12 times 10 is , and we have the negative, plus 54 over Let's think about how we would write this using our function notation. You can't be in two of these intervals.

Let's think about how we would write this using our function notation. So, when x is equal to 10, sorry, when x is equal to negative 10, so we would have negative zero, actually let me write it this way.

## Piecewise function graph

So this is the same thing. It's defined by this line over this interval for x, this line over this interval of x, and this line over this interval of x. Well we see, the value of the function is It looks like stairs to some degree. So we're actually able to fill it in, and then when x is negative one, negative one plus seven is going to be positive six. So that's why it's important that this isn't a -5 is less than or equal to. If it was less than or equal, then the function would have been defined at x equals -9, but it's not. Well, let's see if we can graph it. Over that interval, what is the value of our function? Then, let's see, our function f x is going to be equal to, there's three different intervals. Let me do it over here where I do the, so we're going to have negative 0. We started x equals negative two, when x equals negative two negative two plus seven is, negative two plus seven is five. We have graphed this function that has been defined in a piecewise way. Now this first interval is from, not including -9, and I have this open circle here.

So, that's that interval right over there. It could've, but we see, so there we have it. If it was less than or equal, then the function would have been defined at x equals -9, but it's not. We have just constructed a piece by piece definition of this function. So we're actually able to fill it in, and then when x is negative one, negative one plus seven is going to be positive six. You can't be in two of these intervals. And now let's look at this last interval. That is going to be equal to six. This last interval, when x is negative one, you're going to have, well, this is just going to be positive 12 over 11 'cause we're multiplying it by negative one, plus 54 over 11 which is equal to 66 over 11 which is equal to positive six.

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