The Graph of f(x)=a^x

The graph of f(x)=a^x is defined as being an exponential function. That just means that the function contains a variable expressed as an exponent.



Graph courtesy of http://www.bced.gov.bc.ca/irp/mathk7/icons/f26.gif.


As can be seen from the graph, there is a horizontal asymptote at y = 0, and a vertical asymptote at x = 3. It passes through the points (2, 3.2) and (-1, .75).

There are some phase shift properties to be aware of.

a) f(x)= (a^x)- 1 -> The graph looks just the same, excpet that the graph and horizontal asymptote are shifted down one unit.

b) f(x)= a^(x-1) -> The graph is the same as a^x but it is shifted one unit to the right.

c) f(x)= -a^x -> The graph is the exact same (not moved up or down or left to right) but is flipped directly across the x-axis.