[list][*]Use the input box or slider tools for [math]a[/math] and [math]n[/math] to set the values of the coefficient and power, respectively. [/*][*]Use the input box for [math]x_0[/math] and slider tool for [math]h[/math] to set the locations of the points [math]P[/math] and [math]Q[/math] on the graph to visualize the rate of change of the power function at different points on its graph. [/*][/list]

[b]Power functions[/b] have the form [math]f(x)=ax^n[/math], where [math]a[/math] is a constant called the [b]coefficient [/b]and [math]n[/math] is a constant [b]power[/b]. [br][br]The power [math]n[/math] determines the shape of the graph. There are several categories of power functions with similar graph shapes. [br][list][*]When n is a positive, odd integer (e.g., [math]n=1,3,5,\ldots[/math]). [/*][*]When n is a positive, even integer (e.g., [math]n=2,4,6,\ldots[/math]). [/*][*]When n is a negative, odd integer (e.g., [math]n=-1,-3,-5,\ldots[/math]). [/*][*]When n is a negative, even integer (e.g., [math]n=-2,-4,-6,\ldots[/math]). [/*][*]When n is a fraction (e.g., [math]n=1/2,1/3,3/2,\ldots[/math]). [/*][/list][br]While the power [math]n[/math] gives the shape of the graph, the coefficient [math]a[/math] can stretch/shrink the graph vertically and reflect the graph across the [math]x[/math]-axis (if [math]a<0[/math]).