How to Find Intercepts of a Piecewise Function


How to find the intercepts of a piecewise function. I'm Bon Crowder with, 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 Enjoy it.

Bon Crowder has taught math to over 15,000 adults in living rooms, classrooms and conferences.