precal answer ch3.pdf - C H A P T E R 3 Exponential and Logarithmic Functions Section 3.1 Exponential Functions and Their Graphs 265 Section 3.2

precal answer ch3.pdf - C H A P T E R 3 Exponential and...

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C H A P T E R 3 Exponential and Logarithmic Functions Section 3.1 Exponential Functions and Their Graphs . . . . . . . . . 265 Section 3.2 Logarithmic Functions and Their Graphs . . . . . . . . 273 Section 3.3 Properties of Logarithms . . . . . . . . . . . . . . . . . 281 Section 3.4 Exponential and Logarithmic Equations . . . . . . . . . 289 Section 3.5 Exponential and Logarithmic Models . . . . . . . . . . 303 Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
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265 C H A P T E R 3 Exponential and Logarithmic Functions Section 3.1 Exponential Functions and Their Graphs You should know that a function of the form where is called an exponential function with base a . You should be able to graph exponential functions. You should know formulas for compound interest. (a) For n compoundings per year: (b) For continuous compoundings: A Pe rt . A P 1 r n nt . a 1, a > 0, f x a x , Vocabulary Check 1. algebraic 2. transcendental 3. natural exponential; natural 4. 5. A Pe rt A P 1 r n nt 1. f 5.6 3.4 5.6 946.852 2. f x 2.3 x 2.3 3 2 3.488 3. f 5 0.006 4. f x 2 3 5 x 2 3 5 0.3 0.544 5. 1767.767 g x 5000 2 x 5000 2 1.5 6. 1.274 10 25 200 1.2 12 24 f x 200 1.2 12 x 7. Increasing Asymptote: Intercept: Matches graph (d). 0, 1 y 0 f x 2 x 8. rises to the right. Asymptote: Intercept: Matches graph (c). 0, 2 y 1 f x 2 x 1 9. Decreasing Asymptote: Intercept: Matches graph (a). 0, 1 y 0 f x 2 x 10. rises to the right. Asymptote: Intercept: Matches graph (b). 0, 1 4 y 0 f x 2 x 2 11. Asymptote: y 0 x 3 2 1 1 2 3 5 4 3 2 1 1 y f x 1 2 x x 0 1 2 4 2 1 0.25 0.5 f x 1 2
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266 Chapter 3 Exponential and Logarithmic Functions 12. Asymptote: x 3 2 1 1 2 3 5 4 3 2 1 y y 0 f x 1 2 x 2 x x 0 1 2 1 2 4 0.5 0.25 f x 1 2 13. Asymptote: x 3 2 1 1 2 3 5 4 3 1 1 y y 0 f x 6 x x 2 1 0 1 2 36 6 1 0.167 0.028 f x 14. Asymptote: x 5 4 3 3 2 1 1 2 3 2 1 1 y y 0 f x 6 x x 2 1 0 1 2 0.028 0.167 1 6 36 f x 15. Asymptote: x 3 2 1 1 2 3 5 4 3 2 1 1 y y 0 f x 2 x 1 x 0 1 2 1 2 0.5 0.25 0.125 f x 1 2 16. Asymptote: y 3 x 7 6 5 4 2 1 1 1 2 3 2 3 4 5 y f x 4 x 3 3 x 0 1 2 3 4 3.25 3.063 3.016 3.004 f x 1 17. Because the graph of g can be obtained by shifting the graph of f four units to the right. g x f x 4 , g x 3 x 4 f x 3 x , 18. Because the graph of g can be obtained by shifting the graph of f one unit upward. g x f x 1, f x 4 x , g x 4 x 1 19. Because the graph of g can be obtained by shifting the graph of f five units upward. g x 5 f x , g x 5 2 x f x 2 x , 20. Because the graph of g can be obtained by reflecting the graph of f in the y -axis and shifting f three units to the right. ( Note: This is equivalent to shifting f three units to the left and then reflecting the graph in the y -axis.) g x f x 3 , f x 10 x , g x 10 x 3
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Section 3.1 Exponential Functions and Their Graphs 267 21. Because the graph of g can be obtained by reflecting the graph of f in the x -axis and y -axis and shifting f six units to the right. ( Note: This is equivalent to shifting f six units to the left and then reflecting the graph in the x -axis and y -axis.) g x f x 6 , f x 7 2 x , g x 7 2 x 6 22.
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