# Graphs of exponential functions

Categories: exponentials

We can calculate the value of *a ^{x}* for any rational value of

*x*, where

*a*is a positive value, as described here. We can also find the value of

*a*for irrational values of

^{x}*x*as shown here.

This allows us to plot a graph of the exponential function for any positive value of *a*.

## Exponential function with base 2

This graph shows the function $y = 2^x$:

It shows values of *x* from -3 to 3, in steps of 1/2. These steps can be calculated as described above for fractional exponents.

As with all exponential graphs, the graph gets steeper as *x* increases

## Exponential function with base 10

This graph shows the function $y = 10^x$:

Notice that this graph is a lot steeper than the graph of $y = 2^x$. The two graphs have different x-scales.

## See also

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