The graph of the rational function $\frac{q(x)}{2x^5+x^4-7x^2+1}$ has a horizontal asymptote. What is the largest possible degree of $q(x)$?
To answer this question, I need to recall what it means for a rational function to have a horizontal asymptote. A rational function has a horizontal asymptote if the degree of the numerator is less than or equal to the degree of the denominator. In this case, the degree of the denominator is $5$, so the degree of the numerator must be at most $5$. Therefore, the largest possible degree of $q(x)$ is $5$. 