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Properties of f( x ) = b x
1. The graph of f( x ) will always have the point (0,1). Or put another way, f(0) = 1 in spite of of the value of b.
2. For every possible b bx= 0 . Note that it implies that bx ≠ 0 .
3. If 0 < b < 1 then the graph of bx will decrease as we move from left to right. Verify the graph of ( 1 /2)x above for verification of this property.
4. If b = 1 then the graph of bx will enhance as we move from left to right. Verify the graph of 2x above for verification of this property.
5. If bx= b y then x = y
All of these properties in spite of the final one can be verified simply from the graphs in the first instance.
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