Question

What are the horizontal asymptotes of the function f(x) = 3x² + 4 / 2x ² - x + 7? a) There are no horizontal asymptotes

b) y = 3 / 2
c) y = 3
d) y = 2

Answer 1

The horizontal asymptote of the function f(x) = (3x² + 4) / (2x² - x + 7) is y = 3/2.

Step-by-step explanation:

The function f(x) = (3x² + 4) / (2x² - x + 7) is a rational function. To find the horizontal asymptotes, we need to compare the degrees of the numerator and denominator.

The degree of the numerator is 2 and the degree of the denominator is also 2. When the degrees are the same, the horizontal asymptote can be found by dividing the leading coefficients of the numerator and denominator. In this case, the leading coefficient of the numerator is 3 and the leading coefficient of the denominator is 2.

Therefore, the horizontal asymptote of the function is y = 3/2.