Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Name Section 9.2 Graphing Simple and Rational Functions Date PD Goal: Graph simple rational functions 1) 2) 3) The examples above are known as rational functions. Rational functions take the form p(x) and q(x) polynomials and will learn more about these next year). where We describe the graph of rational functions as hyperbolas (you Every general hyperbola, has the following properties: , The x-axis is a horizontal asymptote. The y-axis is a vertical asymptote. The domain and range are all nonzero real numbers. The graph has two symmetrical parts called branches. For each point (x, y) on one branch, there is a corresponding point (-x, -y) on the other branch. All rational functions of the form and have graphs that are hyperbolas with asymptotes at . Practice: Find the vertical ( ) and horizontal ( and range. Then graph the function by hand. ) asymptotes of the following. State the domain To graph: Use a dotted line to represent the asymptotes. Plot a couple of points on each side of the vertical asymptote. Draw the branches approaching the asymptotes. 1) y 1 2 x3 2) y 2 3 x4 Functions of the form are also hyperbolas, have a vertical asymptote at the x-value that makes the denominator zero, and a horizontal asymptote at Practice: Find the asymptotes of the following functions, state the domain and range, and sketch each graph. 1) y x2 3x 4 2) y 4x 8 x5 3) y x 1 2x 4 4) y 3x 2 6x 1