Intro to Exponential and Logarithmic Functions
Compare the following
Note: These are all examples of increasing exponential functions.
Reflection 1: How can you tell by the equation that the function is an increasing function?
Reflection 2: In general, the larger the base value
Reflection 3: What would the graph of an exponential function with base โ1โ look like
2. Compare the Following
Note: These are all examples of decreasing exponential functions.
Reflection 1: How can you tell by the equation that the function is an decreasing function
For y = a b^[c ( xโh )] + k
1. How does โaโ affect the graph?
a) When a>0?
b) When a<0?
2. How does โcโ affect the graph?
3. How does โhโ affect the graph?
4. How does โkโ affect the graph
Compare The Following
Complete the tables of values:
What do you notice?
Examine and discuss the following graph:
RECALL: List the properties of functions and their inverse (Hint: examine the graphs above)
To refer to the new graph as "the inverse of the exponential function" is awkward. It is also difficult to deal with a function with y as an exponent. For these two reasons a new vocabulary was invented.
Therefore the inverse of
And in general, the inverse of is
Example 1: Determine the inverse of each function
a)ย ย ย ย
b) ย ย ย ย ย ย ย ย ย ย ย
c)
Example 2:
Graph and its inverse