1. Objectives: Students will be able to… Graph simple rational functions Determine domain and range of rational functions

2. where p(x) and q(x) are polynomial functions, and q(x)≠0.

3. Look at table of values What do you notice? What does the graph look like? Set your Δtbl to.0001. What do you notice about the y values as you approach x = 0??

4. Called a hyberbola x axis is called a horizontal asymptote (will never actually touch the x axis, but will get really, really close) y axis is called a vertical asymptote (will never actually touch the y axis) Domain: x ≠o; Range: y ≠o Graph is symmetric

5. Vertical asymptote: x = h (restriction in the domain!!!!) Horizontal asymptote: y = k (restriction in the range!!!!) Domain: x ≠h Range: y ≠ k

6. 1.) Draw asymptotes VA: x = 1; HA: y = 2 2.) Make a table of values (pick a few x values to the left and right of VA) 3.) Plot points and draw curve DOMAIN: x ≠1; RANGE: y ≠2 x2340 y53.531/2

7. DOMAIN: x ≠4; RANGE: y ≠3

8. The horizontal asymptote is: The vertical asymptote is x value that makes the denominator 0 (set denominator = 0 and solve)

9. VA: x = -1 HA: y = 1/3 Make table of values: DOMAIN: x ≠0; RANGE: y ≠1/3 x-3-202 y5/64/3-2/30

11. Write an example of a rational function whose graph is a hyperbola with a vertical asymptote at x = 2 and a horizontal asymptote at y = 1.