a. g(x)= 2x^4 + 1. The highest power in this function, 4, is even so the graph is an even function so end behavior is as x approaches negative infinity, y approaches infinity and as x approaches infinity, y approaches infinity. Sometimes called "up, up" behavior.

b. f(x)= 4x-5x^3. Because both powers are odd, this is an odd function. As you can as x gets larger, the entire function gets smaller. So as x approaches infinity, f(x) approaches negative infinity. Because the function is odd, it has the opposite behavior as x approaches negative infinity.