# Graphing logarithmic and exponential functions

### Exponential graphs

As with graphing other functions, follow the same rules:

- Select a relevant domain.
- Draw up the table of values.
- Plot the points.

For example, plot the curve \(y=2^x\):

\(x\) | \( -3\) | \( -2\) | \(-1\) | \(\ 0\ \) | \(\ 1\ \) | \(\ 2\ \) | \(\ 3\ \) |

\(y = 2^x \) | \(0.125\) | \(0.25\) | \(0.5\) | \( 1\) | \(2\) | \(4\) | \( 8\) |

- Simple exponential growth graphs all have the same shape as the figure above.
- The range includes only real numbers greater than zero.
- There will be a \(y\)-intercept, in this case \(y=1\).
- As the independent variable decreases (approaches negative infinity, \( -\infty \)) the dependent variable approaches zero.
- As the independent variable increases (approaches infinity) the dependent variable increases rapidly.