Learning Resources
Lesson
Up to this point you have considered exponential functions of the form 
where x has been a natural number (i.e. 0, 1, 2, 3, 4, ...) . What happens when x = 0 or x < 0 ?
In this investigation, which you should complete in your offline time and be prepared to discuss in class with your teacher or classmates, you will find out what happens when x = 0 and when x is a negative integer.
Using the graphing technology available, complete the investigation and investigation questions from the Activities section.
Go to the next page if you require further clarification for the investigation.
Using your graphing technology, graph the required equations. Make sure to copy sketches of your graphs form Step A as well as the tables from Step B into your notebook for further analysis.
Make note that the common point to these three graphs can be found from the graphs or from the table of values. This point is called the focal point - the point that all exponential functions of the form have in common.
Note that the decimal representations form of the y-values will have to be converted to fractional form. Recall for terminating decimals use the place value to write a fraction and reduce appropriately. For example, to convert 0.75 to a decimal, write it as 
and reduce it to 
. If the decimal is non-terminating or repeating, use the TI-83, to convert to a fraction. Simply enter as many digits of the decimal as possible, select the MATH key to obtain its menu and select the first item Frac by using the keypad or ENTER key. Press ENTER and the fraction equivalent will appear.
The results of the investigation and its questions should lead you to these facts:
- a zero exponent will give a y-value of 1 regardless of the base used.
- a negative exponent is evaluated by raising the base to the positive of the exponent and taking its reciprocal.
Activity
Investigation Questions p.119. Complete 34, 35, 36 and 37
When you have completed these questions, ask your on-site teacher to get the solutions for you from the Teacher's Resource Binder and check them against your answers. After you do this, if there is something you had trouble with and still do not understand, contact your on-line teacher for help.
After you do the assigned activities, continue on to the Test Yourself section below for a quick quiz on this lesson.
Test Yourself
Graph 
with a TblStart = -3 and 
Tbl = 1 . Describe the effect of the negative exponents on the base.
Suggested solution.