Question

Find the horizontal asymptote of f(x) = 18x² - 7x + 9 / (3x² - 12).

1) y = 2
2) y = 6
3) y = -2
4) y = -6

Answer 1

The horizontal asymptote is y = 6.

Step-by-step explanation:

To find the horizontal asymptote of the function f(x) = (18x² - 7x + 9) / (3x² - 12), we need to determine the behavior of the function as x approaches positive infinity and negative infinity. In this case, the degree of the numerator and denominator is the same, so the horizontal asymptote is determined by the ratio of the leading coefficients.

The leading coefficient of the numerator is 18 and the leading coefficient of the denominator is 3. Thus, the horizontal asymptote is y = 18/3 = 6.

Therefore, the correct answer is y = 6.