2 Rational Function A function of the form where p(x) & q(x) are polynomials and q(x)≠0.
3 Hyperbola A type of rational function. x=0A 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
4 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.
5 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.
6 Ex: Graph State the domain & range. Vertical Asymptote: x=1Horizontal Asymptote: y=2x yLeft of vert. asymp.Right of vert. asymp.Domain: all real #’s except 1.Range: all real #’s except 2.
7 Ex: Graph State domain & range. Vertical asymptote:3x+3=0 (set denominator =0)3x=-3x= -1Horizontal Asymptote:x yDomain: All real #’s except -1.Range: All real #’s except 1/3.
Your consent to our cookies if you continue to use this website.