Oct. 31 Class

Today we talked about how to graph the exponential function.

Handouts:
Graphing Exponential Functions (page 1)
Graphing Exponential Functions (page 2-3)

An exponential function is a function of the form: .

Where b is any base that is greater than zero and not equal to 1 (forgot to mention that in class!  Remind me to tell everyone tomorrow.)

The graph of  looks like the following:

Where I've highlighted some important points that you might use to graph it.

Some important features of this graph include:

• Always increasing.
• Always above zero.
• As x becomes larger, y gets very large.
• As x becomes more negative, y gets closer to zero.
• Never touches the x-axis (a horizontal asymptote).

Next we graphed , and got,

Which turns out to be a horizontal reflection of the above graph.  Points to note:

• The reciprocal of the base is the same thing as a horizontal reflection.
• The y-intercept is always 1 for any base.

Lastly, if you had a table of values and tried to calculate the first and second differences, you will not be able to tell if it's an exponential function.  Instead you must calculate the ratios of each y-value to the y-value before it.  If the ratios are constant then you have an exponential function.

Homework:

Complete the page of the handout for .

P. 243 # 1 - 2.