How to Find Intercepts of a Piecewise Function

How to find the intercepts of a piecewise function. I'm Bon Crowder with MathFour.com, and we're going to look at this piecewise function and find the intercepts. So there are two intercepts to find. There's the y intercept and the x intercepts. So y intercept is where we intercept the y axis somewhere. So that means the x value is zero. So we look in our domain list and we say where is x equal to zero. Here we have x is less than one, x is between one and three, three to eight and bigger than eight. Zero is here at x is less than one. So what we want is f of zero at x plus one. So zero plus one. So zero one is my y intercept. The x intercepts are a little tricky because there could be more than one. So what we have to do is find the x intercept of each piece of our piece wise function and then see if that x intercept is in the domain section. So looking at the first one where is x plus one equal to zero. Well at x equals negative one. Where is x minus two equal to zero. At x equals two. And how about negative two x plus eight. Where is that equal to zero. That is at now I have to do a little bit of work. So I have negative two x is negative eight and divide by two so x if four. And then I have where is x minus one equal to zero and that's at x equals one. So my options are negative one, two, four, and one. So is negative one in here. It is. So that's one of my x intercepts. Is two in here. Holy cow it is. That's one of my x intercepts. Things are looking really good. Is x equal four in here. Three to eight, four lives there. So that's another one of the x intercepts. And x equal one is that in here. Not quite. So x equal one is not one of our x intercepts for the full function because it doesn't live in this domain. And that's how you find the intercepts of the piecewise function. I'm Bon Crowder with MathFour.com. Enjoy it.