Graph all vertical and horizontal asymptotes of the rational function.
F(x)=4/3x-9
The given rational function is F(x) = 4 / (3x - 9).
Vertical Asymptote:
To find the vertical asymptote of the function, we set the denominator equal to zero and solve for x:
3x - 9 = 0
3x = 9
x = 3
Therefore, the vertical asymptote of the function is x = 3.
Horizontal Asymptote:
To find the horizontal asymptote of the 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 denominator is higher than the degree of the numerator, there is no horizontal asymptote.
Therefore, the vertical asymptote of the function is x = 3 and there is no horizontal asymptote.