What are the vertical and horizontal asymptotes for the function f of x is equal to the fraction with numerator 3 x squared and denominator x squared minus 4 ?

For f(x) = 3x²/(x² − 4), factor the denominator: x² − 4 = (x − 2)(x + 2). The denominator is zero at x = −2 and x = 2, so these are the vertical asymptotes. Since the numerator and denominator have the same degree, the horizontal asymptote is the ratio of their leading coefficients, 3/1 = 3. Therefore, the answer is D: horizontal asymptote y = 3 and vertical asymptotes x = −2 and x = 2.

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