Final answer:
The equations of the asymptotes for g(x) = (2x^2+1) / (x+3) are y = 2x.
Step-by-step explanation:
To determine the equations of the asymptotes of the function g(x) = (2x^2+1) / (x+3), we need to look at the behavior of the function as x approaches positive and negative infinity.
As x approaches positive infinity, the term with the highest degree in the numerator and denominator dominates, which is x^2 in this case. So the function behaves like y = 2x^2 / x = 2x as x approaches positive infinity.
As x approaches negative infinity, the term with the highest degree again dominates, so the function behaves like y = 2x^2 / x = 2x as x approaches negative infinity as well.
Therefore, the equations of the asymptotes for g(x) are y = 2x. Option A is the correct answer.