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# Module 23

### Exponential Functions

To solve equations, what formula is used? b^x=b^y
To make this formula possible, the base "b" must be... Positive, so b^x IS a real number for all real numbers x.
Functions of the form are... f(x)=b^x, where b>0.
If b>0, b is NOT 1, and x is a real number, f(x)=b^x is called.. Exponential Function
When graphing... Find and plot a few ordered pair solutions. Set up a table of values for each two functions. Then, connect a smooth curve.
One-to-one function y-intercept (0,1) no x-intercept f(x)=b^x, for b>1
domain: (-infinity,infinity) range: (0,infinity) f(x)=b^x, for 0<b<1
The uniqueness of b^x can be used when: b>0 and b DOES NOT = 1, then... b^x=b^y IS equivalent to x=y.
When solving, each side of the equation must have.. the same base, b^x=b^y
We have equal exponents when the bases are the same and non-negative, this is called... Uniqueness of b^x
An example of the uniqueness of b^x is: 2^x=16, thus we would change 16 to 2^4 so x would equal... x=4
Created by: hannah96lee