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Unformatted text preview: = 2
è2ø
è1ø
0 0 f ( 0) = 2 = 1 æ1ö
g ( 0) = ç ÷ = 1
è2ø 1 f (1) = 2 = 2 æ1ö 1
g (1) = ç ÷ =
è2ø 2 2 f ( 2 ) = 22 = 4 æ1ö 1
g (1) = ç ÷ =
4
è2ø 0 1 1 2 Here is the sketch of the two graphs. Note as well that we could have written g ( x ) in the following way,
x 1
æ1ö
g ( x ) = ç ÷ = x = 2 x
2
è2ø
Sometimes we’ll see this kind of exponential function and so it’s important to be able to go
between these two forms.
Now, let’s talk about some of the properties of exponential functions. Properties of f ( x ) = b x
© 2007 Paul Dawkins 281 http://tutorial.math.lamar.edu/terms.aspx College Algebra 1. The graph of f ( x ) will always contain the point ( 0,1) . Or put another way, f ( 0 ) = 1
regardless of the value of b.
2. For every possible b b x > 0 . Note that this implies that b x ¹ 0 .
3. If 0 < b < 1 then the graph of b x will decrease as we move from left to right. Check out
x æ1ö
the graph of ç ÷ above for verification of this property.
è2ø
4. If b > 1 the...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
 Spring '12
 MrVinh

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