When you are done with this section, you will be able to do the following
- Sketch
the graph of an exponential function.
- Find basic characteristics of an exponential function (domain,
range,
intercepts, increasing/decreasing behavior).
- Write formulas of transformed exponential functions,
- Use an exponential model to solve an application problem (in particular, models involving the natural exponential function and compound interest formulas).
- Use the compound interest formula to solve finance problems.
A good place to find information about exponential functions is your text book (pages 379-397 in College Algebra 3rd edition by Stewart, Redlin, and Watson).
Read carefully:
- x-intercepts are found in the same way we found x-intercepts before (set the function equal to 0 and solve). All x-intercepts are of the form (x, 0). A non-transformed exponential function will have no x-intercepts.
- y-intercepts are found by plugging in 0 for x and
solving. All y-intercepts are of the form (0, y).
- The book mentions the "natural" exponential function. This is just like all other exponential functions. Its base is the number e.
- You will want to take note of when an
exponential function is increasing and when an exponential function is
decreasing.
- ASU First Year Math Exponential Functions lecture notes
- Exponential
Functions*
- Exponential Functions
- Expnonetial
Functions (this has a link to a java applet that will let you
explore transformations of the exponential function)
- MathHelp
Notebook on Exponentail Functions
- Exponential Functions
- Paul's
Online Math Tutorials and Notes
- College Algebra Tutorial on Exponential Functions
- Purplemath - Your Algebra Resource: Exponential Functions I
- Purplemath - Your Algebra Resource: Exponential Functions II
- Purplemath - Your Algebra Resource: Exponential Functions III
- Purplemath - Your Algebra Resource: Exponential Functions IV
Exponent Review
Exponential Functions Homework:
The Exponential Functions Homework contains 7
problems.
Things to remember:
For this particular topic, there are not additional also recommended homework problems.
© 2005 Elizabeth E. K. Jones and the ASU
Department of
Mathematics and Statistics - All rights reserved.
Things to remember:
- Domains must be written as intervals. [ and ] indicate that the endpoint is included. ( and ) indicate that the endpoint is not included. Click here for a review of interval notation.
- Intercepts are points and must be written as ordered pairs (x-intercepts look like (x, 0) and y-intercepts look like (0, y)).
- The range of a function is all possible output values. Ranges must be written as intervals. [ and ] indicate that the endpoint is included. ( and ) indicate that the endpoint is not included. Click here for a review of interval notation.
- NEVER round until the end of your problem.
- ALWAYS put parentheses around your exponent. If your answer is correct when you plug in 1 and not for any of the others, lack of parentheses is the most likelyproblem.
Example 1: similar to problem 5 Example 2: similar to problem 6 Example 3: can help with problems 3 and 4
For this particular topic, there are not additional also recommended homework problems.