Education Technology

Graphing Exponentials

Published on 08/29/2011

Activity Overview

Investigate the graphs of the family of exponential functions.

Objectives

  • Infer why the conditions b > 0 and  b ≠ 0 are necessary for the function to be exponential
  • Determine that for x > 1 the function is increasing and for 0 < x < 1 the function is decreasing
  • Determine that the y-intercept is always (0,1) and there is no x-intercept
  • Determine that for b > 1 the function approaches infinity as x approaches infinity and that for 0 < b < 1 the function approaches infinity as x approaches -infinity
  • Identify the domain as (-infinity, inifinity) and the range as (0, infinity)
  • Identify the equation of the function’s horizontal asymptote as y = 0

Vocabulary

  • Exponential function
  • End behavior
  • Intercepts
  • Domain and range
  • Asymptotes
  • Increasing and decreasing functions

About the Lesson

Students will investigate the graphs of the family of exponential functions f(x) = bx. As a result, students will:

  • Infer why the conditions b > 0 and b ≠ 0 are necessary.
  • Determine how the value of b affects the increasing or decreasing behavior of the function.
  • Determine the y-intercept, domain, and range.
  • Describe the end behavior.
  • State the equation of the asymptote.