Question

What are the asymptotes and removable discontinuities, if any, of `f(x)=(3x-2) / (x+1)`?

Answer 1

vertical asymptote x = -1
horizontal asymptote y = -3

Explanation:

Vertical asymptote can be found when the denominator of

the rational function is zero.

here: x + 1 = 0 gives x = - 1

[Horizontal asymptote can be found when the degree of the

numerator and the degree of the denominator are equal. ]

here , the degree of numerator and denominator are both 1 .

To find the equation take the ratio of leading coefficients.

hence y = `3/1` ie y = 3

graph{(3x-2)/(x+1) [-20, 20, -10, 10]}