Answer
x-int: (1,0)
y-int: (0, -2)
Vertical Asymptote: x=-2
Horizontal Asymptote: y=4
Domain: (-∞, -2) U (-2, ∞)
Range: (-∞, 4) U (4, ∞)
Graph is below.
Work Step by Step
$r(x) = \frac {4x-4}{x+2}$
4x-4 = 0
x = 1
Thus, the x-intercept is at (1,0)
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 = 0
x = -2
So, domain is from (-∞, -2) U (-2, ∞)
Horizontal asymptote is the ratio of the constants of the leading term (with equal degree), which is 4/1 = 4
Thus, the horizontal asymptote is at y=4
So the range is from (-∞, 4) U (4, ∞)
