Graph all vertical and horizontal asymptotes of the rational function.
F(x)=-5/-4x-10
The rational function can be written as F(x) = 5/(4x+10).
Vertical asymptote: Since the denominator of the rational function is (4x+10), the vertical asymptote occurs when 4x+10 = 0. Solving for x, we get x = -10/4 = -5/2. So, the vertical asymptote is x = -5/2.
Horizontal asymptote: To find the horizontal asymptote of the rational function, we compare the degrees of the numerator and denominator. The degree of the numerator is 0 and the degree of the denominator is 1. Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.
Therefore, the vertical asymptote is x = -5/2 and the horizontal asymptote is y = 0.
Graph of the rational function showing the vertical asymptote at x = -5/2 and the horizontal asymptote at y = 0:
Asymptotes:
- Vertical asymptote at x = -5/2
- Horizontal asymptote at y = 0