Logarithmic functions are inverses of exponential functions. To graph a logarithmic function: 1. Identify the inverse exponential form. 2. Create a table of values for the exponential form. 3. Invert the ordered pairs. 4. Plot the points and sketch the graph of the logarithm. Logarithmic functions can be transformed through stretching, compression, reflection, horizontal translation, and vertical translation compared to the parent logarithmic function. Examples are shown to demonstrate how transformations alter the graph.

1. 7.3 LOGARITHMIC
FUNCTIONS AS
INVERSES
Part 2: Graphing Logarithms

2. Logarithms
 A logarithmic function is the inverse of an
exponential function.
 and are inverses
 The graphs of inverse functions are always
reflections across the line y = x

3. Graphing Logarithms
1. Identify the inverse exponential form
2. Create a table of values for the exponential
form (sketch the exponential form)
3. Invert the ordered pairs
4. Plot the points and sketch the graph of the
logarithm

4. Example: Graph each logarithmic
function

5. Example: Graph each logarithmic
function

6. Properties/Transformations of Logarithmic
Functions
 Parent:
 General Form:
 Stretch:
 Compression (shrink):
 Reflection:
 Horizontal Translation:
 Domain:
 Range: All Real Numbers
 Vertical Asymptote:
 Vertical Translation:

7. Example
Describe how the graph of each function
compares with the graph of the parent
function.

8. Example
Describe how the graph of each function
compares with the graph of the parent
function.

9. Homework
 P456 #36 – 43 all, 61 – 67 odd, 73 – 76 all