8.2 The Reciprocal Function Family Honors

The Reciprocal Functions The Reciprocal function f(x) = x ≠0 D: {x|x ≠ 0} R: {y|y ≠ 0} Va: x = 0 Ha: y = 0

Rational Function A function of the form where p(x) & q(x) are polynomials and q(x)≠0. *Graphs are hyperbolas Goal: Graph simple rational functions

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.) y = k (horiz.)

Ex: Graph State the domain & range. Vertical Asymptote: x = 1 Horizontal Asymptote: y = 2 x y Domain: all real #’s except 1.{x|x ≠ 1} Range: all real #’s except 2. {y|y ≠ 2}

Sketch the graph Vertical asymptote: Horizontal asymptote: Domain: Range: x = -3 y = -1 {x|x ≠ -3} {y|y ≠ -1}

YOU TRY! Sketch the graph, give domain, range, vertical and horizontal asymptotes.

Hyperbola (continued) Second form: Vertical asymptote: Set the denominator equal to 0 and solve for x. Horizontal asymptote:

Ex: Graph State domain & range. Vertical asymptote: 3x+3=0 (set denominator =0) 3x=-3 x= -1 Horizontal Asymptote: x y Domain: {x|x ≠ -1} Range: {y|y ≠ 1/3}

Example Sketch the graph, give the domain, range, vertical and horizontal asymptotes. Vertical asymptote: Horizontal asymptote: Domain: Range: x = 2 y = 1/2 {x|x ≠ 2} {y|y ≠ ½}

YOU TRY! Sketch the graph. Give the domain, range, horizontal and vertical asymptotes.

Exit Ticket Sketch the graph, give domain, range, vertical & horizontal asymptotes