Learning Outcomes
By the end of this lesson, you will be able to:
- Determine whether an exponential function and its associated graph represents growth or decay.
- Sketch a graph of an exponential function.
- Graph exponential functions shifted horizontally or vertically and write the associated equation.
- Graph a stretched or compressed exponential function.
- Graph a reflected exponential function.
- Write the equation of an exponential function that has been transformed.
As we discussed in the previous section, exponential functions are used for many real-world applications such as finance, forensics, computer science, and most of the life sciences. Working with an equation that describes a real-world situation gives us a method for making predictions. Most of the time, however, the equation itself is not enough. We learn a lot about things by seeing their visual representations, and that is exactly why graphing exponential equations is a powerful tool. It gives us another layer of insight for predicting future events.