Display Graphing a Function and Its Inverse Function The graph of a function

Display graphing a function and its inverse function

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Display: Graphing a Function and Its Inverse Function The graph of a function and its inverse are symmetric about the line y = x . Why do you think that this is so? EXAMPLE 6 If f ( x ) = 3 x 2, find f 1( x ). Graph f and f 1 on the same set of axes. Draw the line y = x as a dashed line for reference. Solution f ( x ) = 3 x 2 y = 3 x 2 x = 3 y 2 x + 2 = 3 y begin numerator x plus 2 end numerator over 3 equals y f to the 1 open parenthesis x close parenthesis power equals begin numerator x plus 2 end numerator over 3 Page 33 of 47 Print | Beginning & Intermediate Algebra 1/31/2014 ...
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PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. Now we graph each line. We see that the graphs of f and f 1 are symmetric about the line y = x . If we folded the graph paper along the line y = x , the graph of f would touch the graph of f 1. Try it. Redraw the functions on a separate piece of graph paper. Fold Student Practice 6 If f open parenthesis x close parenthesis equals 1 over 4 x plus 1 comma find f 1 ( x ). Graph f and f 1 on the same coordinate plane. Draw the line y = x as a dashed line for reference. 709710 11.4 Exercises Verbal and Writing Skills, Exercises 1–6 Complete the following: 1. A one-to-one function is a function in which no ordered pairs _____________________________. 2. If any horizontal line intersects the graph of a function more than once, the function ____________________. 3. The graphs of a function f and its inverse f 1 are symmetric about the line __________. 4. Do all functions have inverse functions? Why or why not? 5. Does the graph of a horizontal line represent a function? Why or why not? Does it represent a one-to-one function? Explain. 6. Does the graph of a vertical line represent a function? Why or why not? Does it represent a one-to-one function? Explain. Indicate whether each function is one-to-one. 7. B = {(0, 1), (1, 0), (10, 0)} 8. A = {( 6, 2), (6, 2), (3, 4)} 9. 10. C = {(12, 3), ( 6, 1), (6, 3)} 11. E = {(1, 2.8), (3, 6), ( 1, 2.8), (2.8, 1)} Page 34 of 47 Print | Beginning & Intermediate Algebra 1/31/2014 ...
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PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted. 12. F = {(6, 5), ( 6, 5), (5, 6), ( 5, 6)} Indicate whether each graph represents a one-to-one function. 13. 14. 15. 16. 17. Page 35 of 47 Print | Beginning & Intermediate Algebra 1/31/2014 ...
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PRINTED BY: [email protected] Printing is for personal, private use only. No part of this book may be reproduced or transmitted without publisher's prior permission. Violators will be prosecuted.
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