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5.4 Logarithmic Functions

5.4 Logarithmic Functions. Quiz. What’s the domain of f(x) = log x?. Logarithmic Functions . Standard Form: Log a x = y , a > 0, a ≠ 1 Graphs of Logarithmic Functions: . Properties. 1. Domain: (0, ∞) 2. Range: (- ∞, ∞ ) 3. Asymptote: y-axis is the vertical asymptote

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5.4 Logarithmic Functions

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  1. 5.4 Logarithmic Functions

  2. Quiz • What’s the domain of f(x) = log x?

  3. Logarithmic Functions • Standard Form: Logax = y , a > 0, a ≠ 1 • Graphs of Logarithmic Functions:

  4. Properties • 1. Domain: (0, ∞) • 2. Range: (-∞, ∞) • 3. Asymptote: y-axis is the vertical asymptote • 4. Key Points: (a, 1), (1, 0), and (a-1, -1)

  5. Find the Domain of the Functions • f(x) = log4(x - 3) • g(x) = log(x2 - 9) • h(x) = log5x + 1

  6. Graphs by transformations • h(x) = log2(x - 3) • f(x) = lnx - 2

  7. Finding Inverse Functions of an Exponential Function • f(x) = -2x + 3 • g(x) = -10x + 4

  8. Homework • Page 358: 1, 5, 9-18(M3), 33, 36, 39, 45, 54, 57, 62, 66, 67 • KEY: 18, 45, 57, 66 • Reading: 5.5 Exponential and Logarithmic Equations and Inequalities

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