Exponential Functions

Overview

Description

The equation of an exponential function can be written in the form f(x)=abxf(x) = ab^x, where a0a\neq 0, b>0b>0, and b1b\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 xx approaches infinity or negative infinity. All exponential functions can be graphed as transformations of the parent function f(x)=bxf(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.