Answer
x-intercept: (-2,0)
y-intercept: (0, -2/3)
Vertical Asymptote: x=-3, 1
Domain: (-∞, -3) U (-3, 1) U (1, ∞)
Horizontal Asymptote: y=0
Range: (-∞, ∞)
See graph below
Work Step by Step
$r(x)=\frac{x+2}{(x+3)(x-1)}$
$x+2 = 0$
x = -2
x-intercept: (-2,0)
y-intercept is the ratio of the constants, which is 2 / -3 = -2/3
Thus, the y-intercept is at (0, -2/3)
Vertical asymptotes are when the denominator is equal to 0
$(x+3)(x-1) = 0$
x = -3, 1
So, domain is from (-∞, -3) U (-3, 1) U (1, ∞)
Horizontal asymptote is the ratio of the constants of the leading term (with equal degree)
0 (since top degree is not 2, unlike bottom)
Thus, the horizontal asymptote is at y=0
So the range is from (-∞, ∞)