Graphing Log FunctionsPre-Calculus

Graphing Logarithms

Objectives: Make connections between log functions

and exponential functions Construct a table of values for a log

function Graph a log function

Vocabulary: logarithms, natural logarithms

How do you graph a logarithmic function?Graph f(x) = log3 xThis is the inverse of g(x) = 3x

x g(x)

-2-1 0 1 2

1/91/3 1 3 9

x f(x)

-2-1 0 1 2

1/91/3 1 3 9 f(x) = log3 x

g(x) = 3x

Graphing Logarithms

Steps to Graph a Log Function•Condense your log function.•Rewrite the function as an exponential

equation•Make a table for exponential function•Invert values for log function•Plot the points•Connect with a curve

Asymptotes???•Use this example of a log function to

determine if there would ever be a domain restriction.

Asymptotes•You can only take the log of positive

numbers!

•So, your domain restriction is the solution to the inequality:

(what’s getting logged) > 0

Example•Graph the equation:

Domain:

Range:

Example•Graph the equation:

Domain:

Range:

Example•Graph the equation:

Domain:

Range:

Example•Graph the equation:

Domain:

Range:

Homework•WB: p.57-58 odd