Answer
x-intercept: (2,0)
y-intercept: (0, 2)
Vertical Asymptote: x=-2, 1
Domain: (-∞, -2) U (-2, 1) U (1, ∞)
Horizontal Asymptote: y=0
Range: (-∞, ∞)
See graph below
Work Step by Step
$r(x)=\frac{2x-4}{x^2 + x -2}$
$2x-4 = 0$
x = 2
x-intercept: (2,0)
y-intercept is the ratio of the constants, which is -4/-2 = 2
Thus, the y-intercept is at (0, 2)
Vertical asymptotes are when the denominator is equal to 0
$x^2 + x -2 = 0$
$(x+2)(x-1) = 0$
x = -2, 1
So, domain is from (-∞, -2) U (-2, 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 (-∞, ∞)