Notice that the

graph from Example 1 and this

graph increase to the right of the

y-axis and decrease to the left. Both graphs,

pass through the

point (0, 1). The reason for that, remember, is that any non-zero real number raised to the 0 power has a value of 1. If both graphs are drawn on the same axes, it can be seen that although the two graphs are very similar, they are not exactly the same.

The

graph of

is the one whose distance becomes further away from the

y-axis as it increases. That is because it increases at a slower

rate than the other. The larger the real number used as the base, the faster its graph, values of

, will increase.

Notice that the

graph in Example 1 approaches the

x-axis as the x values decrease (the

graph going to the left). The x-axis,

equation y = 0 is an asymptote. This is because

is always positive. There is no value of x which can make

negative or zero. As the values of x decrease, so do the values of

, but there is a limit which the

graph will never reach, the x-axis.

**Example 2:** Consider the following example: Using the same values for x, let’s graph this exponential function whose exponent is negative. Coordinates of several points are shown in the table below.

*x* | *f(x)* |

-2 | 9 |

-1 | 3 |

0 | 1 |

1 | |

2 | |

The graph of this function is decreasing since it begins higher on the left side of the y-axis and continuously decreases in value as it moves toward and crosses over the y-axis. The graphs of functions in the form will be decreasing.