Sec 11-1 Graphs of Exponential and Logarithmic Functions

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Presentation transcript:

Sec 11-1 Graphs of Exponential and Logarithmic Functions

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?

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?

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

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

Log examples to try… Y = log4 (1/16) Y = log10 (-10) 2 = logb (16) 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”

More Log Examples Log(1/2)c = -3 Logx (9) = (2/3) Loga (1) = x Ax = 1 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”

Write the equations in log form 3y = 12 y = log3 (12) A5 = 100 5 = loga (100) 4log4(16) = x Log4x = log416 What is aloga(x)? X And loga(ax) = x “y is the power of 3 that yields 12”

HW: 477-479, #7-25(odd), 29,31,33,39,41,45