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.