2. Copyright © 2007 Pearson Education, Inc. Slide 4-2 Chapter 4: Rational, Power, and Root Functions 4.1 Rational Functions and Graphs 4.2 More on Graphs of Rational Functions 4.3 Rational Equations, Inequalities, Applications, and Models 4.4Functions Defined by Powers and Roots 4.5 Equations, Inequalities, and Applications Involving Root Functions

3. Copyright © 2007 Pearson Education, Inc. Slide 4-3 4.1 Rational Functions and Graphs Rational function – quotient of two polynomials p(x) and q(x), with q(x)  0. Examples

4. Copyright © 2007 Pearson Education, Inc. Slide 4-4 The simplest rational function – the reciprocal function 4.1 The Reciprocal Function

5. Copyright © 2007 Pearson Education, Inc. Slide 4-5 4.1 The Reciprocal Function

6. Copyright © 2007 Pearson Education, Inc. Slide 4-6 4.1 Transformations of the Reciprocal Function The graph of can be shifted, translated, and reflected. Example Graph SolutionThe expression can be written as Stretch vertically by a factor of 2 and reflect across the y-axis (or x-axis).

7. Copyright © 2007 Pearson Education, Inc. Slide 4-7 4.1 Graphing a Rational Function Example Graph Solution Rewrite y: The graph is shifted left 1 unit and stretched vertically by a factor of 2.

8. Copyright © 2007 Pearson Education, Inc. Slide 4-8 4.1 The Rational Function f (x) = 1/x 2

9. Copyright © 2007 Pearson Education, Inc. Slide 4-9 4.1 Graphing a Rational Function ExampleGraph Solution Vertical Asymptote: x = –2; Horizontal Asymptote: y = –1.

10. Copyright © 2007 Pearson Education, Inc. Slide 4-10 4.1 Mode and Window Choices for Calculator Graphs Non-decimal vs. Decimal Window –A non-decimal window (or connected mode) connects plotted points. –A decimal window (or dot mode) plots points without connecting the dots. Use a decimal window when plotting rational functions such as –If y is plotted using a non-decimal window, there would be a vertical line at x = –1, which is not part of the graph.

11. Copyright © 2007 Pearson Education, Inc. Slide 4-11 4.1 Mode and Window Choices for Calculator Graphs Illustration Note: See Table for the y-value at x = –1: y 1 = ERROR.