The document discusses exponential functions and how to work with tables of exponential functions. It explains that an exponential function has the general form f(x) = a*b^x or f(x) = a*b^-x, where a is the starting value and b is the growth or decay factor. It provides instructions for making a table of values for an exponential function by inputting integer x-values and outputting the corresponding y-values found by multiplying the previous term by b. Examples are given of completing tables and writing the exponential function given a table of x and y-values.

1. 3.2 Exponential Function
Tables

2. General Form
• The general form of an exponential
function is
or
where a ≠ 0, b > 0, and b ≠ 1.
• a is the starting value
• b is the growth/decay factor

3. Making a Table
• To make a table for an exponential
function:
• input values start at 0 and increase by 1
• output values start at a and are
multiplied by b
**Can also plug inputs into the equation
to find outputs!**

4. Example 1:
• Complete the function table for
x
f(x)

5. You Try!
• Complete the function table for
x
g(x)

6. Writing a Function
• To write an exponential function from a
table:
• Find f(0). This is a.
• Divide to find the growth/decay factor.
This is b.
• Plug into

7. Example 2:
• Write an exponential function for the table:
x
f(x)
0
2
1
8
2
32
3
128

8. Example 3:
• Write an exponential function for the table:
x
g(x)
1
6
2
12
3
24
4
48

9. You Try!
• Write a function for the table:
t
h(t)
-1
0.25
0
1
1
4
2
16