WARM-UP

1. WARM-UP Mixed Review p. 563 # 43-51

2. Algebra 2 Check: p. 577 # 3-7, 24-42 (x3)(12 pts) Objective(8.2): Graph simple rational functions.

3. Rational Function • A function of the form where p(x) & q(x) are polynomials and q(x)≠0.

4. Hyperbola x=0 • A type of rational function. • Has 1 vertical asymptote and 1 horizontal asymptote. • Has 2 parts called branches. (blue parts) They are symmetrical. We’ll discuss 2 different forms. y=0

5. Hyperbola (continued) • One form: • Has 2 asymptotes: x=h (vert.) and y=k (horiz.) • Graph 2 points on either side of the vertical asymptote. • Draw the branches.

6. Ex 1: a) Graph State the domain & range. Vertical Asymptote: x=1 Horizontal Asymptote: y=2 x y -5 1.5 -2 1 0 -1 2 5 4 3 Left of vert. asymp. Y-intercept Domain: all real #’s except 1. Range: all real #’s except 2. Right of vert. asymp.

7. Ex 1: b) Graph State the domain & range. Vertical Asymptote: x=-2 Horizontal Asymptote: y=-3 • x y • -7 -4 • -3 -8 • 0 -1/2 • -2 Left of vert. asymp. Right of vert. asymp. Domain: all real #’s except -2. Range: all real #’s except -3.

8. Hyperbola (continued) • Second form: • Vertical asymptote: Set the denominator equal to 0 and solve for x. • Horizontal asymptote: • Graph 2 points on either side of the vertical asymptote. Draw the 2 branches.

9. Ex 2: a) GraphState domain & range. Vertical asymptote: 3x+3=0 (set denominator =0) 3x=-3 x= -1 Horizontal Asymptote: x y -3 .83 -2 1.33 0 -.67 2 0 Domain: All real #’s except -1. Range: All real #’s except 1/3.

10. Ex 2: b) GraphState domain & range. Vertical asymptote: 2x+3=0 (set denominator =0) 2x=-3 x= -3/2 Horizontal Asymptote: x y -5 3 -2 9 0 -1/3 2 1 Domain: All real #’s except -3/2. Range: All real #’s except 2.

11. Classworkon graph paper Guided practice: p. 559 # 2-5

12. Homework

13. Closure