Chapter 8

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FURTHER Your Understanding 1. Sketch a graph of the inverse of each exponential function. a) c) f (x) 5 a 1 x f (x) 5 4 x 3 b 8.1 b) f (x) 5 8 x d) f (x) 5 a 1 5 b x 2. Write the equation of each inverse function in question 1 in i) exponential form ii) logarithmic form 3. Compare the key features of the graphs in question 1. 4. Explain how you can use the graph of y 5 log 2 x (at right) to help you determine the solution to 2 y 5 8. 5. Write the equation of the inverse of each exponential function in exponential form. a) c) y 5 a 1 x y 5 3 x 4 b b) y 5 10 x d) y 5 m x 6. Write the equation of the inverse of each exponential function in question 5 in logarithmic form. 4 y y = log 2 x 2 x –2 0 –2 2 4 6 8 10 –4 –6 –8 7. Write the equation of each of the following logarithmic functions in exponential form. a) y 5 log 5 x c) y 5 log 3 x b) y 5 log 10x d) y 5 log1 4 8. Write the equation of the inverse of each logarithmic function in question 7 in exponential form. 9. Evaluate each of the following: a) log 2 4 c) log 464 e) b) log 3 27 d) log 5 1 f) log 2 a 1 2 b log 3 !3 10. Why can log 3 (29) not be evaluated? 11. For each of the following logarithmic functions, write the coordinates of the five points that have y-values of 22, 21, 0, 1, 2. a) y 5 log 2 x b) y 5 log 10 x NEL <strong>Chapter</strong> 8 451
8.2 Transformations of Logarithmic Functions YOU WILL NEED • graphing calculator GOAL Determine the effects of varying the parameters of the graph of y 5 a log 10 (k(x 2 d)) 1 c. INVESTIGATE the Math The function f (x) 5 log 10 x is an example of a logarithmic function. It is the inverse of the exponential function f (x) 5 10 x . y 10 8 f (x) = 10 x y = x 6 4 2 f (x) = log 10 x x –2 0 2 4 6 8 10 –2 ? How does varying the parameters of a function in the form g(x) 5 a log 10 (k(x 2 d)) 1 c affect the graph of the parent function, f(x) 5 log 10 x? A. The log button on a graphing calculator represents log 10 x. Graph y 5 log 10 x on a graphing calculator. Use the window setting shown. Communication Tip If there is no value of a in a logarithmic function (log a x), the base is understood to be 10; that is, log x 5 log 10 x. Logarithms with base 10 are called common logarithms. B. Consider the following functions: • y 5 log 10 (x 2 2) • y 5 log 10 (x 2 4) • y 5 log 10 (x 1 4) Make a conjecture about the type of transformation that must be applied to the graph of y 5 log 10 x to graph each of these functions. C. Graph the functions in part B along with the graph of y 5 log 10 x. Compare each of these graphs with the graph of y 5 log 10 x. Was your conjecture correct? Summarize the transformations that are applied to y 5 log 10 x to obtain y 5 log 10 (x 2 d ). 452 8.2 Transformations of Logarithmic Functions NEL
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Page 3 and 4: 8 Getting Started Study Aid • For
Page 5 and 6: 8.1 Exploring the Logarithmic Funct
Page 7: In Summary Key Ideas • The invers
Page 11 and 12: Reflecting L. Describe the domain a
Page 13 and 14: EXAMPLE 2 Connecting a geometric de
Page 15 and 16: PRACTISING 4. Let f (x) 5 log 10 x.
Page 17 and 18: Solution B: Using a graphing calcul
Page 19 and 20: c) log 2 (24) 5 x Determine the exp
Page 21 and 22: EXAMPLE 4 Selecting a strategy to e
Page 23 and 24: CHECK Your Understanding 1. Express
Page 25 and 26: 17. The doubling function y 5 y 0 2
Page 27 and 28: log a (mn) 5 x 1 y m 5 a x so log a
Page 29 and 30: APPLY the Math EXAMPLE 4 Selecting
Page 31 and 32: EXAMPLE 6 Selecting strategies to s
Page 33 and 34: 9. Write each expression as a singl
Page 35 and 36: Study • See Lesson 8.2, Examples
Page 37 and 38: 8.5 Solving Exponential Equations G
Page 39 and 40: Solution C: Solving the equation gr
Page 41 and 42: EXAMPLE 4 Solve 2 x11 5 3 x21 to th
Page 43 and 44: 8. Solve for x. a) 4 x11 1 4 x 5 16
Page 45 and 46: Reflecting A. What strategies for s
Page 47 and 48: x 2 2 9 5 2 4 x 2 2 9 5 16 x 2 5 25
Page 49 and 50: 9. The loudness, L, of a sound in d
Page 51 and 52: APPLY the Math EXAMPLE 1 Solving a
Page 53 and 54: EXAMPLE 2 Representing exponential
Page 55 and 56: Solution Sound Loudness (dB) soft w
Page 57 and 58: 6. Calculate to two decimal places
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8.8 Rates of Change in Exponential
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EXAMPLE 2 Selecting a strategy for
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Solution -2 Tangents to y = 10 x y
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y 8 y = log x - 1 6 2 d 4 2 y = - 1
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PRACTICE Questions Lesson 8.1 1. De
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8 Chapter Self-Test 1. Write the eq
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2(sec 2 x 2 tan 2 x) 9. 5 sin 2x se
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d) D 5 5xPR 0 x . 06, R 5 5 yPR6 e)
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17. log b x!x 5 log b x 1 log b !x
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value of x. Determine the average r
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Chapter 8

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