Alg 1 11.8 pg 694

GOAL 2GRAPHING RATIONAL FUNCTIONSThe inverse variation models you graphed in Lesson 11.3 are a type of rationalfunction. A rational function is a function of the formƒ(x) = p olynomial.polynomialIn this lesson you will learn to graph rational functions whose numerators anddenominators are first-degree polynomials. Using long division, such a functioncan be written in the formay = + k. x º hRATIONAL FUNCTIONS WHOSE GRAPHS ARE HYPERBOLASaThe graph of the rational function y = + k xº his a hyperbola whose center is (h, k).The vertical and horizontal lines through the centerare the asymptotes of the hyperbola. An asymptoteis a line that the graph approaches. While the distancebetween the graph and the line approaches zero, theasymptote is not part of the graph.Branchesof thehyperbolayCenter(h, k)AsymptotesxEXAMPLE 5Graphing a Rational FunctionSketch the graph of y = 1 x +2.1SOLUTION Think of the function as y = + 2. You can see that the centerx º 0is (0, 2). The asymptotes can be drawn as dashed lines through the center. Make atable of values. Then plot the points and connect them with two smooth branches.xyº4 1.75º2 1.5º1 1º0.5 00 undefined0.5 41 32 2.54 2.255y4(0, 2)31y x 2135 xIf you have drawn your graph correctly,it should be symmetric about the center(h, k). For example, the points (0.5, 4) and(º0.5, 0) are the same distance from thecenter (0, 2), but in opposite directions.692 Chapter 11 Rational Equations and Functions