Function y=x^n, where n is natural number, is called power function with natural exponent.
When n=1, we obtain function y=x; when n=2, we obtain parabola y=x^2; when n=3, we obtain cubic parabola y=x^3.
Let n is any even natural number greater than two: n=4, 6, 8, ... . In this case function y=x^n has same properties as y=x^2. Graph of such function resembles parabola, but for |x|>1 this function grows faster and appeares closer to y-axis; when |x|<1, the bigger n the closer graph to x-axis (see left figure).
Let n is any odd natural number greater than three: n=5, 7, 9, ... . In this case function y=x^n has same properties as y=x^3. Graph of such function resembles cubic parabola, but the bigger n the more steeply parts of graphs up and down. When |x|<1, the bigger n the closer graph to x-axis (see right figure).