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So what is a piecewise function?

According to google, a piecewise function is:

“A function defined by multiple sub-functions, each sub-function applying to a certain interval of the main function’s domain.”

Yeah, or in English it means a function that is broken up into multiple parts.

Of course, we can’t really write a piece wise function the way we normally write a regular function; and this is why we make sure to show the different parts of a piece wise function.

Again, this is one of those times where explaining how to work with a piece wise function is much harder than just showing.

So here’s an example

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SOLVING A PIECE WISE FUNCTION

So let’s say we are given a graph as such

Let’s take a look at what we have:

We know when x goes from 0 – 5, the graph goes up. �So, we find what that linear equation is.

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So how do we read a piece wise function?

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And that’s essentially it

That’s pretty much it!

So a piece wise function is a longer function with a few conditions attached to it.

So, there are quite a few things we can do with them, but to elaborate a little more, here’s another example.

(This time, we’ll work backwards.)

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BUT THAT MAKES SENSE, RIGHT?

I mean, let’s look at the graph and see if that makes sense.

That’ll tell us if we’re on the right track or not.

So here’s the graph:

So we know our answer must be right because when we look at the graph, we can see that when x is 4, y is -1.

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LET’S TRY ANOTHER

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Again, we just look at it

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The “plugging it in” method

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Reading the graph method

They asked for h(9), so now we look at the graph, follow when x = 9.

As we can see, when x = 9, y = 1.

So, h(x) still equals 1.

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PROS AND CONS OF BOTH METHODS

Pro of the Plugging it in method

Don’t have to graph the equations

Cons

It’s easy to make a mistake trying to calculate the actual answer.

Pros of graphing

Easy to read