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?[br]
Reflection 2: In general, the larger the base value[br]
Reflection 3: What would the graph of an exponential function with base “1” 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 ( x−h )] + k
1. How does “a” affect the graph?[br]
a) When a>0?[br]
b) When a<0?[br]
2. How does “c” affect the graph?[br]
3. How does “h” affect the graph?[br]
4. How does “k” 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 [math]y=2^x[/math]
And in general, the inverse of [math]y=a^x[/math] is
Example 1: Determine the inverse of each function
a) [math]y=10^x[/math]
b) [math]y=log_{_{_3}}X[/math] [br] [br]
c)[i] [math]y=\frac{1}{2}^x[/math][br][/i]
Example 2:
Graph [math]y=log_{_{_6}}X[/math]and its inverse