Final answer:
The horizontal asymptote of the function f(x) = x³ / (5x³ - 40) is y = 1/5, as it's determined by the ratio of the leading coefficients of the numerator and denominator. The correct answer is c) y = 1/5.
Step-by-step explanation:
The student has asked about the horizontal asymptotes of the function f(x) = x³ / (5x³ - 40). To find horizontal asymptotes, we compare the degrees of the numerator and denominator of the rational function. If the degrees are equal, like in this case where both the numerator and denominator have a degree of 3, the horizontal asymptote will be the ratio of the leading coefficients. Here, both the numerator and denominator are x³, so their coefficients are 1 and 5, respectively.
Therefore, the horizontal asymptote is y = 1/5, as the coefficients (1 for the numerator and 5 for the denominator) dictate the horizontal asymptote's equation. Thus, the correct answer is c) y = 1/5.