Embedded Files
Transformation Rules
Exponential functions have the same behavior as polynomial functions.
An exponential function is a function, and like all functions, it has its methods of determining the domain, range, and intercepts.
The same can be said for graphing. What works for other functions will apply to exponential functions.
00:00
Properties of Negative Exponents
We know if b-1 = (1/b)1 also, (m/n)-1 = (n/m)1.
It is important to change all negative exponents into standard form.
Example 1
f(x) = (2/3)-x + 1 - 2 in standard form becomes f(x) = (3/2)x - 1 - 2.
Looking at the standard form of this exponential equation, the following is true: a > 0 and b > 1 .
Therefore (according to the table above) f(x) is a growth function and is increasing.
Example 2
f(x) = -(5/2)-(x + 1) - 2 in standard form becomes f(x) = -(2/5)x + 1 - 2
Looking at the standard form of this exponential equation, the following is true: a < 0 and 0 < b < 1 .
Therefore (according to the table above) f(x) is a decay function and is increasing.
Google Sites
Report abuse