# 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

## Join the GraphicMaths Newletter

Sign up using this form to receive an email when new content is added:

## Popular tags

angle area cartesian equation chord circle combinations complex polygon cosh cosine cosine rule cube decagon derivative diagonal directrix dodecagon ellipse equilateral triangle exponent exponential exterior angle focus gradient hendecagon heptagon hexagon horizontal hyperbola hyperbolic function interior angle inverse hyperbolic function irregular polygon isosceles trapezium isosceles triangle kite locus major axis minor axis newton raphson method nonagon normal octagon parabola parallelogram parametric equation pentagon perimeter permutations power pythagoras proof quadrilateral radius rectangle regular polygon rhombus root sine sine rule sinh sloping lines solving equations solving triangles square standard curves star polygon straight line graphs symmetry tangent tanh transformations trapezium triangle vertical