# Exponential Functions

## Overview

### Description

The equation of an exponential function can be written in the form $f(x) = ab^x$, where $a\neq 0$, $b>0$, and $b\neq1$. The graph of an exponential function is either strictly increasing or strictly decreasing. The graph has a horizontal asymptote, which is a horizontal line that the curve approaches as $x$ approaches infinity or negative infinity. All exponential functions can be graphed as transformations of the parent function $f(x) = b^x$. A data set displayed in a scatterplot may approximate the shape of the graph of an exponential function. Technology can be used to generate an exponential function that best fits the data.

### At A Glance

• The rule for an exponential function includes a variable as an exponent.
• The base of an exponential parent function determines whether the function is increasing or decreasing.
• Transformations can be used to graph exponential functions.
• Exponential growth and decay can be modeled using exponential functions. Exponential growth has an increasing exponential function, while exponential decay has a decreasing exponential function.
• Technology can be used to generate an exponential function that best fits the exponential relationship between two variables.