The function seems to be y = (x+1) / (x -1)^2
1) key number
The key number (also called critical values) is where the denominator equals zero.
(x -1)^2 = 0 => x = 1
2) intervals: (-∞,1) ,(1,∞)
3) Sign of the function
The sign of the denominator is always positive, then the sign of the function is the same sign of the numerator
x +1 > 0 => x > - 1
x+ 1 < 0 => x < -1
Then in the interval (-∞,1) the function is negative for (-∞,-1) and positive for (-1,1).
The function is positive for all the values in the interval (1,∞)
Briefle, the functionis negative in (-∞,-1) and positive in (-1,∞).
