9.2 Graphing Simple Rational Functions Obj: to graph a hyperbola Do Now: What value(s) would make this function undefined? x = -4 and y = -7

Rational Function is a function of the form where p(x) & q(x) are polynomials and q(x)≠0. DO NOT COPY THIS SLIDE!

Hyperbola Is the graph of a type of rational function has a vertical asymptote and a horizontal asymptote (imaginary boundary lines) has 2 symmetrical parts called branches x=0 y=0 Vertical asymptote Horizontal asymptote

One form: Has 2 asymptotes: vertical is at x=h (whatever makes the denominator zero) horizontal is at y=k To graph, plot 2 points on either side of the vertical asymptote & draw the branches. *We’ll discuss 2 different forms of rational functions*

Ex 1: Graph then state 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 v.a. Right of v.a.

HW:

continued… Obj: to graph a hyperbola Do Now: What value of x would make this function undefined? x = -5/2y = 1/2

Second form: Has 2 asymptotes: vertical: set the denominator = 0 and solve for x. horizontal: To graph, plot 2 points on either side of the vertical asymptote & draw the branches. *2 different forms of rational functions*

Ex 2: Graph then 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