# 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.

### Interactive Tutorial

Your browser is completely ignoring the <APPLET> tag!

1. Click on the button above "click here to start" and maximize the window obtained.

2. Use the slider to change parameter a and compare the domains of both functions.

3. Use the slider to change parameter a and compare the ranges of both functions.

4. Use different values of a and explain which type of functions grows faster as x takes larger positive values.

5. Change a and examine the interval(s) of increase and decrease of the types of functions. Conclude.

6. Does the exponential function have an x intercept? Change a and examine the x intercept of the power function.

7. Compare the y intercept of the graphs of the two types of functions.