Final answer:
A monomial graph when n is even will show that both ends of the graph move in the same direction, there will be a maximum or minimum point at x = 0, and the graph will be continuous and smooth.
Step-by-step explanation:
Three characteristics of a monomial graph when n is even include:
- The ends of the graph will move in the same direction, either both up or both down, because even functions are symmetric with respect to the y-axis.
- At x = 0, the graph will have either a maximum or minimum point, since an even-powered monomial has its vertex at the origin.
- The graph is continuous and smooth, without any sharp turns or cusps. This results from the nature of polynomial functions, which are differentiable everywhere in their domains.