College Algebra, Chapter 4, 4.2, Section 4.2, Problem 76

Portions of the graphs of $y = x^2, \quad y = x^3, \quad y = x^4, \quad y = x^5$ and $y = x^6$ are plotted in the figure below. Determine which function belongs to the graph.



If the graph is symmetric to the $y$-axis, then its exponent must be an even number. And if the value of the exponent increases, then the graph of even exponent function became flatter near 0. On the other hand, if the graph is symmetric to the origin, then its exponent must be an odd number. And if the value of the exponent increases, then its graph became more steeper near 0. Thus, graph 1 matches $y = x^4$, graph 2 matches $y = x^2$ and graph 5 matches $y = x^5$