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Sec 11-1 Graphs of Exponential and Logarithmic Functions

Sec 11-1 Graphs of Exponential and Logarithmic Functions. What is an exponential function?. F(x) = a x where a is positive and does not equal 1. Graph in your calculator a = 2, 3, and 4. What happens as a gets larger?. F(x) = 4 x is the steepest!. What is the domain? What is the range?.

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Sec 11-1 Graphs of Exponential and Logarithmic Functions

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  1. Sec 11-1 Graphs of Exponential and Logarithmic Functions

  2. What is an exponential function? • F(x) = ax where a is positive and does not equal 1. • Graph in your calculator a = 2, 3, and 4. What happens as a gets larger? F(x) = 4x is the steepest! What is the domain? What is the range?

  3. What if 0 < a < 1? • Graph in your calculator f(x) = ax for a = ½, a = 1/3, a = ¼ and describe what happens. (1/4)x is the steepest. What is the domain? What is the range?

  4. What is the inverse of y = ax ? • X = ay • How do we graph it? • Ex: x = 2y

  5. How do we solve x = ay for y? • Y = loga(x) means x = ay • Example: y = log2(8) • Means: y is the power of 2 that yields 8. What’s y? • i.e. 2y = 8. • Y = 3 • LOG a (x) = Y Exponent Answer Base

  6. Log examples to try… • Y = log4 (1/16) • 4y = (1/16) • Y = -2 • Y = log10 (-10) • 10y = -10 • Impossible • 2 = logb (16) • B2 = 16 • B = 4 only (base must be positive) “y is the power of 4 that yields 1/16” “y is the power of 10 that yields -10” “2 is the power of b that yields 16”

  7. More Log Examples • Log(1/2)c = -3 • (1/2)-3 = c • 8 = c • Logx (9) = (2/3) • X(2/3) = 9 • 27 • Loga (1) = x • Ax = 1 • X = 0 (remember, exponential so x can’t be 1) “-3 is the power of ½ that yields c” “2/3 is the power of x that yields 9” “x is the power of a that yields 1”

  8. Write the equations in log form • 3y = 12 • Log3 (12) = y • A5 = 100 • Loga (100) = 5 • 4log4(16) = x • Log4x = log416 • What is aloga(x)? • X • And loga(ax) = x

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