Graph all vertical and horizontal asymptotes of the rational function.
F(x)=6x+13/4x-2
To determine the vertical asymptotes of a rational function, we set the denominator equal to zero and solve for x:
4x - 2 = 0
4x = 2
x = 1/2
Therefore, the vertical asymptote for F(x) is x = 1/2.
To determine the horizontal asymptote, we compare the degrees of the numerator and denominator of the function:
- The degree of the numerator is 1
- The degree of the denominator is 1
Since the degrees are equal, the horizontal asymptote is the ratio of the leading coefficients:
Horizontal asymptote: y = 6/4 = 3/2
Therefore, the vertical asymptote is x = 1/2 and the horizontal asymptote is y = 3/2.