Compare Exponential and Power Functions
Exponential functions and power functions are compared interactively, using an applet. The properties such as domain, range, x and y intercepts, intervals of increase and decrease of the graphs of the two types of functions are compared in this activity.
The properties of exponential functions of the form
f(x)= a x
and power functions of the form
g(x)= x a
are compared interactively by changing parameter a which is the base in the exponential function and the power in the power function. a takes integer values from 2 to 9.
- Click on the button above "click here to start" and maximize the window obtained.
- Use the slider to change parameter a and compare the domains of both functions.
- Use the slider to change parameter a and compare the ranges of both functions.
- Use different values of a and explain which type of functions grows faster as x takes larger positive values.
- Change a and examine the interval(s) of increase and decrease of the types of functions. Conclude.
- Does the exponential function have an x intercept? Change a and examine the x intercept of the power function.
Compare the y intercept of the graphs of the two types of functions.