College Algebra (Abridged)

1.12 Exponential Functions An exponential function is a function that is written in the form of ( ) = , such that > 0 For example, when = 1 , then ( ) = 1 . If > 1 , then the pattern of -values for different values of will look as follows: Suppose = 2 2 ( ) ( , ) Plotting these values on a graph, we get the following representation:

− 2 2 −2 = 1 4 = 0.25 0.25 ( − 2,0.25) − 1 2 −1 = 1 2 = 0.5 0.5 ( − 1,0.5) 0 2 0 = 1 1 (0,1) 1 2 1 = 2 2 (1,2) 2 2 2 = 4 4 (2,4) 3 2 3 = 8 8 (3,8)

It should be noted that for all values of a, (0) = 1 , since 0 is always equal to one for any value of . Moreover, the value of ( ) will always be positive and greater than 0, since is always greater than 0, and hence, is always greater than zero. There are some rules of exponents that help simplify the exponential expressions: 1. = + 2. ( ) = 3. = − 4. ( ) = 5. � � = , b ≠ 0 6. − = 1 , a ≠ 0 7. 1 = √ 8. = ( √ )

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