# How to Graph a Piecewise Function with Three Inequalities

## Transcript

Hi, I'm Rachel, and today we're going to be going over how to graph a piecewise function with three inequalities. When we are graphing a piecewise function, we are going to have three different pieces in this graph and each piece is going to be bound by an inequality. What does that mean? That means that if we have three graphs like Y equals 3, Y equals X and Y equals X plus 3, we're going to bind these by certain periods on the graph. So we have X is less than negative 2. X is between we'll say negative 2 and 3 and we'll have X being greater than 3. So, when X is less than negative 2, we're going to use this equation on the line. So if here is negative 2, we're going to have an open circle because it's less than but not equal to, so that's going to be everything to the left of negative 2 and that's how that equation looks when graphed. Then, when we have Y equals X, we're going to, that's going to be a line like this right, except when you hit negative 2, you're going to have a circle, right, because that's where it ends in this piece of the graph, but, it's very small but I'm making this or equal to and if it's or equal to, we close in the circle. Here when we get up to 3, it's going to be again an open circle because we are not actually including the 3, it's everything less than 3. Then, for things greater than 3, we're going to use this equation. So when Y, we have to find what Y is when X is 3 well when X is 3, that's 3 plus 3 so that's going to give us Y equals 6 so that's going to look like 3, 6 up here, that will be again an open circle and a line like this if we are graphing X plus 3. And that is the 3 pieces of a piecewise function using our inequalities. I'm Rachel and thank you for learning with me today.