Graphing Exponential Functions | Mathematics
Your understanding of functions is becoming pretty impressive. You’ve already learned how to graph quadratic functions, linear functions, and the domain and range of functions. Let’s keep the momentum going in preparation for the TASC Test Assessing Secondary Completion™ Mathematics subtest by learning how to graph exponential functions.
Understanding Exponential Functions
Exponential functions are similar to quadratic functions in that they involve exponents. But there is one big difference: In exponential functions, the variable represents the power, rather than representing the base. For example:
- Quadratic functions can come in the form of f(x) = ax^{2} + bx + c.
- The variable x is the base and the number 2 was the power.
- Exponential functions, on the other hand, can come in the form of g(x) = 2^{x}.
- The variable x is the power and the number 2 is the base.
Because the variable is the power in exponential functions, they have the ability to grow and decay at a rapid rate.
How to Graph Exponential Functions
Graphing exponential functions is a high emphasis topic on the TASC Mathematics subtest. The Khan Academy offers an example of how these functions are graphed. Let’s take a look:
Graph the exponential function: y = 3^{x}.
To find the graph of this function, follow these steps:
- Determine if the function will grow or decay.
- Make a table of coordinates.
- Create the graph axis.
- Graph the x and y coordinates from the table.
Solution:
- The exponential function y = 3^{x} will grow since the base (3) is a positive number. If the base was a negative number, the exponential function would decay.
- When creating a table of coordinates, choose small, whole numbers for x that are easy to solve for:
y=3^{x}
x |
y |
-2 |
3^{-2} = 1/9 |
0 |
3^{0} = 1 |
1 |
3^{1} = 3 |
2 |
3^{2} = 9 |
3 |
3^{3} = 27 |
4 |
3^{4} = 81 |
- Create the graph axis and plot the x and y coordinates from the table:
You will notice that the function starts as a very small fraction (1/9). This number is too small to be seen on the graph. Because of the nature of exponential functions, the graph grew quickly.
Continue your practice of understanding and graphing exponential functions at the Khan Academy.