Lesson 1.5: Functions and Logarithms AP Calculus Mrs. Mongold.

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Presentation transcript:

Lesson 1.5: Functions and Logarithms AP Calculus Mrs. Mongold

One-to-One Function A function f(x) is one-to-one on a domain D if f(a) f(b) whenever a b  Check using the horizontal line test if it doesn’t pass it is not a one-to-one function.

Inverses Reversing a one-to-one function, the inverse of a function is denoted f -1 (x) Identity function: the result of composing a function and its inverse in either order.  To test if two functions are inverses of one another compute f o g and g o f If (f o g)(x) = (g o f)(x) then f and g are inverses of one another

To find an inverse 1. solve y=f(x) for x in terms of y 2. Interchange x and y, result is y=f -1 (x)

Logarithmic Functions The base a logarithm function y = log a x is the inverse of the base a exponential function y = a x (a>0, a ≠ 1)  The domain of log a x is (0, ∞) the range of a x  The range of log a x is (- ∞, ∞) the domain of a x

Properties of Logarithms Inverse base a Inverse base e Product Rule Quotient Rule Power Rule

Change of Base Formula log a x =log x ÷ log a

Homework Pgs 39-40/ 3-48 multiples of 3