The horizontal asymptote of f(x) = (2x^2+3)/(x^2-4) as x approaches infinity is:

• A. y = 0
• B. y = -2
• C. y = x
• D. y = 2

Answer: (D)

When x is very large in magnitude, the highest-power terms dominate a rational function. Here both the numerator and denominator are degree 2, so the function behaves like the ratio of the leading coefficients: 2x^2/x^2 = 2. This means the graph approaches the horizontal line y = 2 as x → ∞ (and also as x → −∞). Equivalently, you can rewrite f(x) as (2 + 3/x^2)/(1 − 4/x^2), which tends to 2/1 = 2 as x grows without bound. The other options don’t fit this behavior: y = 0 would require the degrees to differ so the leading terms vanish; y = x isn’t horizontal; y = −2 would require a negative leading coefficient. Therefore, the horizontal asymptote is y = 2.