February 22, 2016
5.4 Logarithmic Functions
Day 2
Objectives:
1. Determine the domain of a logarithmic function.
2. Graph logarithmic functions.
February 22, 2016
Logarithms are the inverse
functions of
exponential functions.
February 22, 2016
Exponential Functions:
Logarithms:
Domain:
Range: y > 0
Domain: x > 0
Range:
February 22, 2016
Properties of the Logarithmic Function f(x) = logax
1. The domain is the set of positive real numbers.
The range is the set of all real numbers.
2. There are no y-intercepts and the x-intercept is 1.
3. The y-axis ( x = 0) is a vertical asymptote as
4. The graph contains (1, 0), (a, 1), and (1/a, 1).
February 22, 2016
Recall the natural logarithm,
the base is "e"
We also have the common logarithm,
the base is 10
February 22, 2016
Example 1: Find the domain of each function.
February 22, 2016
Example 2: Graph the function. Determine domain, range
and vertical asymptote.
February 22, 2016
Example 3: Graph the function. Determine domain, range
and vertical asymptote.
February 22, 2016
Homework:
Graphing Logarithms WS
Finish Web Assignment 5.4