Rational Functions, Transformations Chapter 5 Functions 5.6 Rational Functions, Transformations MATHPOWERTM 11, WESTERN EDITION 5.6.1

x y Graphing the Basic Rational Function A rational function is a function of the form where g(x) and h(x) are polynomials and h(x) ≠ 0. Graph x y -10 -1/10 -2 -1/2 -1 undefined 1/2 2 1

Graphing the Basic Rational Function The function is undefined when x = 0. This shows up as an asymptote. Asymptote: a line that a curve approaches but never touches. Vertical asymptote: x = 0 Horizontal asymptote: y = 0 Asymptotes Domain: x ≠ 0, x ϵ R. Range: y ≠ 0, y ϵ R 5.6.7

Rational Functions and Transformations Graph Compare the graph of with Vertical stretch by a factor of 5, horizontal translation 2 units right. Sketch the graph using transformations. The horizontal asymptote is translated 2 units right as well. Domain: x ≠ 2, x ϵ R. Range: y ≠ 0, y ϵ R 5.6.7

Graphing Rational Functions 5.6.8

Compare Rational Equations Consider Describe how this function is related to f(x).

Assignment: p. 442 #1, 3, 4a, 5b, 6, 7c, 8, 10, 13