If f(x)=x-1/(x-2)2 (x+1) which of the following is true about f?

1. The function f is defined for all real numbers except x = 2 and x = -1.
2. The function f has a vertical asymptote at x = 2 and a hole at x = -1.
3. The function f is a rational function.
4. The function f is continuous on its domain.

Vertical Asymptote:

- f has a vertical asymptote at x = 2 because the denominator becomes 0 at that point.

Removable Discontinuity:

- f has a removable discontinuity at x = 1 because the limit of f(x) as x approaches 1 is 0. This means the function can be made continuous at x = 1 by redefining it as f(1) = 0.

Horizontal Asymptote:

- f does not have a horizontal asymptote because the degree of the numerator and denominator are the same.

Slant Asymptote:

- f has a slant asymptote at y = x - 2 because the degree of the numerator is one greater than the degree of the denominator.

Therefore, the correct answer is that f has a vertical asymptote at x = 2, a removable discontinuity at x = 1, and a slant asymptote at y = x - 2.