3.2

Day 2

Logarithmic Functions

– Graph logarithmic functions.

– Find the domain of a logarithmic function.

Pg. 397 # 44, 46, 48-58 even, 76, 78For #54-58 even, you do NOT have to state the asymptoteand you do NOT have to state the domain and range. Make sure to graph f(x) = log2 x and the given function on the same grid. Clearly label each function.

Logarithmic function and exponential function are inverses of each other.This means they are reflections of one another across the line y = x

y = 10x

y = log10x

1. Graph f(x)=3x and g(x)=log3x in the same rectangular coordinate system.

x f(x) = 3x

-2

-1

0

1

2

x f(x) = log3x

-2

-1

0

1

2

Transformations of logarithmic functions are treated as other transformations

• Follow order of operation

• Note: When graphing a logarithmic function, the graph only exists for x>0, WHY? If a positive number is raised to an exponent, no matter how large or small, the result will always be POSITIVE!

Domain Restrictions for Logarithmic Functions

Since a positive number raised to an exponent (pos. or neg.) always results in a positive value, you can ONLY take the logarithm of a POSITIVE NUMBER.

Remember, the question is: What POWER can I raise the base to, to get this value?

DOMAIN RESTRICTION: logby x

such that x > 0

2. Find the domain of f(x) = log4(x-5)

Let’s start today’s assignment together…