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.

Power an Exponential Functions

The properties of exponential functions of the form
f(x)= B x

and power functions of the form
g(x)= x P

are compared interactively, using an html5 applet, by changing the base
B of the exponential function and the power P of the power function.

Interactive Tutorial

 B = 2 P = 2
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1. Change parameters B and P and compare the domains of both functions.
2. Change parameters B and P and compare the ranges of both functions.
3. Use different values of B and P and explain which of the two types of functions grows faster as x takes larger positive values.
4. Change B and P and examine the interval(s) of increase and decrease of the two types of functions. Conclude.
5. Does the exponential function have any x intercept? Change P and examine the x intercept of the power function.
6. Compare the y intercept of the graphs of the two types of functions.