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Warm Up

Warm Up. Make a t-chart for the following functions 3 x 3 -x 3 x + 1. Math IV Lesson 16. Essential : How do you recognize, evaluate, and graph logarithmic functions? Standard: a. Compare and contrast properties of functions within and across the following types: linear, quadratic,

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Warm Up

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  1. Warm Up • Make a t-chart for the following functions • 3x • 3-x • 3x + 1

  2. Math IV Lesson 16 Essential : How do you recognize, evaluate, and graph logarithmic functions? Standard: a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise. b. Investigate transformations of functions

  3. New Vocabulary • Logarithmic form: logba = c • Exponential form: bc = a • Logarithmic function: f(x) = logax • Natural logarithmic function: f(x) = ln(x)

  4. Changing between log form and exponential form We all know 32 = 9 Now lets write it in log form…..

  5. Evaluating logs Solve for x (hint put in exponential form) • log232 = x • Log31 = x • Log42 = x

  6. Properties of logs • loga1 = 0 • Logaa = 1 • Logaax = x • If logax = logay , then x = y

  7. Examples • Solve for x Log2x = log23 Simplify log55x Solve for x Log44 = x

  8. Graphs of logs and exponential equations • Graph both Y = 2x and y = log2x

  9. Natural log ln • F(x) = logex = ln(x) Properties of natural logs • ln1 = 0 because e0 = 1 • Ln (e) = 1 because e1 = e • Lnex = x because elnx = x • If ln(x) = ln(y) then x = y

  10. Using properties of natural logs • Simplify the expressions Ln (1/e) eln5 4ln(1) 2ln(e)

  11. Home work • P203 • 1-17 odd, 25-28,

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