1. Graphs of Rational Functions Hyperbolas and lines (7.9)

2. POD Find the sum.

3. More graphing We’re going to graph rational functions again. Here is the Method: 1. Factor. 2. Determine any holes and vertical asymptotes. 3. Cancel what can be canceled—makes it easier to graph. 4. Plot points. 5. Connect the points. 6. Label asymptotes and holes clearly!

4. Try it Graph First, factor and cancel. Where are the vertical asymptote and hole?

5. Try it Graph Next, use the reduced expression to graph. Make a table– plot quite a few points, and pay particular attention to the area around the V.A. and hole. What does that remaining factor in the top mean?

6. Try it Graph. You should have a graph that looks like this. The vertical asymptote is obviously at x = -3. Where is the hole? Why don’t you see it? Where is the horizontal asymptote?

7. Try it Graph. The vertical asymptote is at x = -3. Hole at x = 1. X-intercept at x = -1. The horizontal asymptote is at y =1.

8. Try it Graph. When you graph this on paper, be sure to sketch in and label the asymptote and draw the hole on the curve. This shape of a curve, with two curves facing each other, is called a hyperbola.

9. Try it again Graph this function. What is different from the last one? What is the shape of this graph?

10. Try it again Graph this function. What is different from the last one? You should have a line with a hole at x = 3.

11. Checking for holes While the graphing calculator may not show holes on the graph, it can show you holes. Hit second-table for this graph. You’ll see ERROR when x=3. If 3 doesn’t show up on the table, you can type it in at the bottom, at x=.