Factoring Practice 1.x 2 – 16 2.x x x 2 – 10x x x (x – 4)(x + 4) (x + 3)(x 2 - 3x + 9) 5(5x 2 + 3) (x – 6)(x – 4) 4(2x – 3)(2x + 3) (3x – 2)(9x 2 +6x + 4)

9.2 Graphing Simple Rational Functions p. 540 What is the general form of a rational function? What does the h & k tell you? What does the graph of a hyperbola look like? What does the graph of ax+b/cx+d tell you? What information does the domain & range tell you?

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

Hyperbola 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. x=0 y=0

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.

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.

Ex: Graph State the domain & range. Vertical Asymptote: x=1 Horizontal Asymptote: y=2 x y Domain: all real #’s except 1. Range: all real #’s except 2. Left of vert. asymp. Right of vert. asymp.

Ex: Graph State domain & range. Vertical asymptote: 3x+3=0 (set denominator =0) 3x=-3 x= -1 Horizontal Asymptote: x y Domain: All real #’s except -1. Range: All real #’s except 1/3.

What is the general form of a rational function? What does the h & k tell you? Asymptotes are x = h, y = k What does the graph of a hyperbola look like? Two symmetrical branches in opposite quadrants. What does the graph of ax+b/cx+d tell you? cx+d = 0 is the vertical asymptote and y = a/c is the horizontal asymptote What information does the domain & range tell you? Domain tells what numbers can be used for x and the range is the y numbers when put into the equation.

Assignment p , even, even