Lesson Objectives

- Learn how to sketch the graph of an exponential function

## How to Sketch the Graph of an Exponential Function

An exponential function is of the form:

f(x) = a

a > 0

a ≠ 1

x is any real number

When we think about the graph of f(x) = a

Example 1: Sketch the graph of each $$f(x) = 3^x$$ Let's create a table with some ordered pairs:

Now we can plot the points on the coordinate plane and connect the points using a smooth curve. As the graph moves from right to left, it approaches the x-axis but does not touch it.

f(x) = a

^{x}a > 0

a ≠ 1

x is any real number

When we think about the graph of f(x) = a

^{x}:- (0,1) is on the graph
- Since a can't be 0, and any non-zero number raised to the power of 0 is 1

- The graph approaches the x-axis, but will never touch it. It forms an asymptote.
- The domain consists of all real numbers or the interval: (-∞, ∞)
- The range consists of all positive real numbers, or the interval: (0, ∞)
- When a > 1, the graph rises from left to right
- When 0 < a < 1, the graph falls from left to right

Example 1: Sketch the graph of each $$f(x) = 3^x$$ Let's create a table with some ordered pairs:

x | y | (x, y) |
---|---|---|

-2 | 1/9 | (-2, 1/9) |

-1 | 1/3 | (-1, 1/3) |

0 | 1 | (0, 1) |

1 | 3 | (1, 3) |

2 | 9 | (2, 9) |

Ready for more?

Watch the Step by Step Video Lesson Take the Practice Test