What are the equations of the asymptotes of the graph of the function f of x is equal to the fraction with numerator 3 x squared minus 2 x minus 1 and denominator x squared plus 3 x minus 10 ?

Factor the denominator: x² + 3x − 10 = (x + 5)(x − 2), so the vertical asymptotes are x = −5 and x = 2. The numerator does not cancel either factor. Since the numerator and denominator have the same degree, the horizontal asymptote is the ratio of their leading coefficients, 3/1 = 3. Thus the asymptotes are x = −5, x = 2, and y = 3, which is choice D.

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