Investigate the graphs of the family of exponential functions.
- 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
- Exponential function
- End behavior
- Domain and range
- 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.