The graph of the rational function $\frac{2x^7-5x^4 + 3x^3 -x+5}{q(x)} $ has a horizontal asymptote. What is the smallest possible degree of $q(x)$?
A horizontal asymptote occurs when the degrees of the numerator and denominator are equal, or when the degree of the denominator is greater than the degree of the numerator. So, the smallest possible degree of $q(x)$ is the same as the degree of the numerator, which is 7. Therefore, the smallest possible degree of $q(x)$ is 7. 