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Understanding Logarithmic Functions: Graphing Transformations and Properties

Explore logarithmic functions, properties, and graphing transformations while solving equations and gaining insights into their domain and range.

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Understanding Logarithmic Functions: Graphing Transformations and Properties

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  1. Logarithmic Functions: Intro & GraphingTS: Making decisions after reflection and review Warm-Up 1) log416 = 2 is the logarithmic form of 4░ = 16 34 = 81 is the exponential form of log ░░ = 4 log464 = log2 ¼ =

  2. Definition of a Logarithmic Function (p.274) For x > 0, a > 0anda ≠ 1, y = logaxif and only ifx = ay Wheref(x) = logaxis called thelogarithmic functionwith basea. Properties of Logarithms (p. 274) • loga1 = 0 because a0 = 1 • logaa = 1 because a1 = a • logaax = x and alogax = x. (Inverse Property) • If logax = logay, then x = y. (One-to-One Property)

  3. Using the Definition to Convert between forms Write each in Write each in exponential form logarithmic form • log3y = -4 1) 2x = 15 • ln b = a 2) e3 = y • log 15 = x 3) 103 = 1000

  4. Evaluate or Solve each logarithmic expression or equation 1) log71/49 Solve for x: 2) log168 1) log2x = log28 3) log0.001 4) log√28 2) log4x = -2 *5) log345 *6) ln 5 3) 3log3x = 7

  5. Logarithmic Functions are inverses of _______________ Given the above graph of y = 4x, graph y = log4x What is the domain & range of y = log4x Given the above graph of y = ex, graph y = ln x What is the domain & range of y = ln x Given the above graph of y = log3x, graph y = log3(x+2) – 3 What is the domain & range of y = log3(x+2)–3

  6. Graphing Using Translations Give the domain and range & graph each. • f(x) = log4(x – 2) + 3

  7. Graphing Using Translations Give the domain and range & graph each. 2) y = -logx – 3

  8. Graphing Using Translations Give the domain and range & graph each. 3) y = 3 + log2(-x + 1)

  9. Graphing Using Translations Give the domain and range & graph each. 4) y = ln(2 – x)

  10. Graphing Using Translations 5)Given the function is a translated form of y=log3x, find the equation of the graph.

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