Graphing Piecewise Functions
These functions are called 'piecewise' because there are different pieces that act differently on the number line. For example, this function has two pieces. F of X simply means Y. The first equation is Y = X - 2 if X < 0. Graph the line starting at -2 on the Y-intercept with a closed dot because there is an equal which means 0 is included. Go up one over one and so on from that point. Since the equation is only if X < 0 you keep the line towards the negative numbers which are less than 0 and erase the rest of the line. The second equation is Y = X + 3 when X > 0. Put an open circle on 3 on the Y-intercept and from there go up and over one. This piece is 'only if X is greater than 0' so keep the line towards the right, where 1, 2, 3, ect. are obviously larger than 0. The reason there are open and closed circles are because the point may or may not be included, and it could not be a function if it did not pass the vertical line test.
This piecewise function has three parts to it which makes it a bit more complex. The first equation is Y = 2X + 2 if X < -2. Graph the inequality as you would any other, starting with an open circle at the Y-intercept 2 and following the slope 2/1. Since it is only if X is less than negative two, there's a horizontal boundary at the -2 on the X-intercept and keep the line to the left of the boundary, then erase the remainder of the line. The next equation is Y = 3 if -2 < X < 3. A horizontal line is drawn at 3 on the Y-intercept. There are two boundaries to this line, at -2 (closed circle) and at 3 (open circle). The final equation is Y = -X if 3 < X. You'd start at the point of origin (0,0) and descend one and go over one. The boundary of this line is at the X-intercept on three and you'd only keep the line drawn to the right of the boundary, with a closed dot on the line because there is an equal.