Exponential functions and power functions can be compared interactively using our HTML5 applet. Key properties such as domain, range, \(x\)- and \(y\)-intercepts, and intervals of increase and decrease are examined side by side.
The properties of exponential functions of the form:
\[ f(x) = B^x \]and power functions of the form:
\[ g(x) = x^P \]are contrasted by changing the base \(B\) of exponential functions and the power \(P\) of power functions.
Interactive Tutorial Applet
Exploration Activities
- Change parameters \(B\) and \(P\) and compare the domains of both functions.
- Change parameters \(B\) and \(P\) and compare the ranges of both functions.
- Use different values of \(B\) and \(P\) and explain which of the two types of functions grows faster as \(x\) takes larger positive values.
- Change \(B\) and \(P\) and examine the interval(s) of increase and decrease of the two types of functions. Conclude.
- Does the exponential function have any \(x\)-intercept? Change \(P\) and examine the \(x\)-intercept of the power function.
- Compare the \(y\)-intercept of the graphs of the two types of functions.