Which phrase describes the end behavior of the graph of ƒ(x) = –x5 – 4x4 + 7x2 – 2?

Well for end behavior, you simply look at the highest exponent (in this case 5) and look for 2 things:
Is it even or odd? Odd
Is it positive or negative? Negative

Using this we can determine that it is up to the left, and down to the right

Or, for more advanced terms, as x approaches -∞, y approaches ∞, and as x approaches ∞, y approaches -∞