1 / 10

Logarithmic Functions: Intro & Graphing TS: Making decisions after reflection and review

Logarithmic Functions: Intro & Graphing TS: Making decisions after reflection and review. Warm-Up 1) log 4 16 = 2 is the logarithmic form of 4 ░ = 16 3 4 = 81 is the exponential form of log ░ ░ = 4 log 4 64 = log 2 ¼ =. Definition of a Logarithmic Function (p.274).

meli
Download Presentation

Logarithmic Functions: Intro & Graphing TS: Making decisions after reflection and review

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related