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7 Exponential and Logarithmic Functions 7.1 Graph Exponential Growth Functions 7.2 Graph Exponential Decay Functions 7.3 Use Functions Involving e 7.4 Evaluate Logarithms and Graph Logarithmic Functions 7.5 Apply Properties of Logarithms 7.6 Solve Exponential and Logarithmic Equations 7.7 Write and Apply Exponential and Power Functions Before In previous chapters, you learned the following skills, which you’ll use in Chapter 7: graphing functions, finding inverse functions, and writing functions. Prerequisite Skills VOCABULARY CHECK Copy and complete the statement using the graph at y the right. 1. The domain of the function is ? . 2. The range of the function is ? . y5 x2213 1 3. The inverse of the function is ? . 1 x SKILLS CHECK Graph the function. State the domain and range. (Review p. 446 for 7.1–7.3.) } } 3} 4. y 5 22Ï x 2 1 5. y 5 Ï x 1 3 6. y 5 Ï x 2 2 1 5 Find the inverse of the function. (Review p. 438 for 7.4.) 7. y 5 3x 1 5 8. y 5 22x3 1 1 1 x2, x ≥ 0 9. y 5 } 2 Write a quadratic function in standard form for the parabola that passes through the given points. (Review p. 309 for 7.7.) 10. (0, 21), (1, 2), (3, 14) 11. (3, 8), (4, 17), (7, 56) 12. (23, 9), (1, 27), (5, 255) 1SFSFRVJTJUFTLJMMTQSBDUJDFBUDMBTT[POFDPN Take-Home Tutor for problem solving help at www.publisher.com 476 n2pe-0700.indd 476 10/14/05 12:20:34 PM Now In Chapter 7, you will apply the big ideas listed below and reviewed in the Chapter Summary on page 538. You will also use the key vocabulary listed below. Big Ideas 1 Graphing exponential and logarithmic functions 2 Solving exponential and logarithmic equations 3 Writing and applying exponential and power functions KEY VOCABULARY • exponential function, • exponential decay • common logarithm, p. 500 p. 478 function, p. 486 • natural logarithm, p. 500 • exponential growth • decay factor, p. 486 • exponential equation, function, p. 478 • natural base e, p. 492 p. 515 • growth factor, p. 478 • logarithm of y with base • logarithmic equation, • asymptote, p. 478 b, p. 499 p. 517 Why? You can use exponential and logarithmic functions to model many scientific relationships. For example, you can use a logarithmic function to relate the size of a telescope lens and the ability of the telescope to see certain stars. Algebra The animation illustrated below for Example 7 on page 519 helps you answer this question: How is the diameter of a telescope’s objective lens related to the apparent magnitude of the dimmest star that can be seen with the telescope? -LOG$ LOG$ %NTERTHEVALUEOF- LOG$ 3UBTRACTFROMBOTHSIDESOFTHEEQUATION

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