What is the limit of the function as x approaches infinity?

Question

(x^4 - 7x + 9) / (4 + 5x + x^3)
From what I know, the limit should be infinity since the greater exponent is in the numerator. However, I am only given the options: 0, (1/4), 1, 4, or Does not exist. Is there an error on the part of the answers given, or am i doing this wrong?

Answer 1

You are right.
as x gets big, the function looks like x^4/x^3 which is x which gets big. Infinity is correct.