Copyright © 2011 Pearson Education, Inc. Slide Rational Functions and Graphs Rational Function A function f of the form p/q defined by where p(x) and q(x) are polynomials, with q(x) 0, is called a rational function. Examples
Copyright © 2011 Pearson Education, Inc. Slide The simplest rational function – the reciprocal function 4.1 The Reciprocal Function
Copyright © 2011 Pearson Education, Inc. Slide The Reciprocal Function
Copyright © 2011 Pearson Education, Inc. Slide 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).
Copyright © 2011 Pearson Education, Inc. Slide Graphing a Rational Function Example Graph Solution Rewrite y: The graph is shifted left 1 unit and stretched vertically by a factor of 2.
Copyright © 2011 Pearson Education, Inc. Slide 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.
Copyright © 2011 Pearson Education, Inc. Slide Mode and Window Choices for Calculator Graphs Illustration Note: See Table for the y-value at x = –1: y 1 = ERROR.
Copyright © 2011 Pearson Education, Inc. Slide The Rational Function f (x) = 1/x 2
Copyright © 2011 Pearson Education, Inc. Slide Graphing a Rational Function ExampleGraph Solution Vertical Asymptote: x = –2; Horizontal Asymptote: y = –1.