How do you determine the asymptotes of #y = (3x)/(x + 4)#?

graph{y = (3x- 1)/(x +4) [-22.8, 22.81, -11.4, 11.4]}

Hopefully this helps!

To determine the asymptotes of the function y = (3x)/(x + 4), we need to consider two types of asymptotes: vertical asymptotes and horizontal asymptotes.

Vertical asymptotes occur when the denominator of the function becomes zero. In this case, the denominator is (x + 4). Setting it equal to zero, we find x = -4. Therefore, the vertical asymptote is x = -4.

Horizontal asymptotes can be determined by analyzing the behavior of the function as x approaches positive or negative infinity. To find the horizontal asymptote, we compare the degrees of the numerator and denominator. In this case, both the numerator and denominator have a degree of 1. Therefore, the horizontal asymptote is y = 3/1, which simplifies to y = 3.

In summary, the asymptotes of the function y = (3x)/(x + 4) are a vertical asymptote at x = -4 and a horizontal asymptote at y = 3.