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 b^{x}= 0 . Note that it implies that b^{x} ≠ 0 .
3. If 0 < b < 1 then the graph of b^{x} 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 b^{x} will enhance as we move from left to right. Verify the graph of 2^{x} above for verification of this property.
5. If b^{x}= 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.