SFM Productions Presents: Another saga in your continuing Pre-Calculus experience! 3.2Logarithmic Functions and their Graphs.

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Presentation transcript:

SFM Productions Presents: Another saga in your continuing Pre-Calculus experience! 3.2Logarithmic Functions and their Graphs

p234#7-31, 37-41, 51-65, 85-91, 95, 97 Homework for section 3.2

exponential horizontal Asymptote y = 0 logarithmic vertical asymptote x = 0

A logarithmic function with base “a”: is denoted by: if and only if:

A logarithm is an exponent. Aan exponent. logarithmis Aan exponent. logarithmis Aan exponent. logarithmis Aan exponent. logarithmis Aan exponent. logarithmis logarithm is exponent.

The two equations are equivalent … Use one to solve the other … and use the other to solve the one … depending upon which one you need to solve. is the same as:

Properties of Common Logarithms logarithmic exponential All this stuff works with e and ln, too.

Properties of Natural Logarithms logarithmic exponential

Another Property of Common and Natural Logarithms

For all: f(x) = log a x Increasing: Decreasing Domain: Range: VA: Intercept:

Shifting f(x) = log 2 x f(x) = log 2 x + 3 f(x) = log 2 x - 4 What is new asymptote???

Shifting f(x) = log 2 x f(x) = log 2 (x + 3) f(x) = log 2 (x - 4) What is new asymptote???

Domain Your favorite … or is it mine??? On your calculators, do: What can you deduce from this??? You can’t take the log of a negative number, or 0. Common or Natural NCD

Finding domains of log functions …

Go! Do!