Answer
x-intercept is at (-3,0)
y-intercept is at (0, 2)
Vertical asymptote: x = 1/2
Domain: (-∞, 1/2) U (1/2, ∞)
Horizontal asymptote: y=-1/3
Range: (-∞, -1/3) U (-1/3, ∞)
Graph is below
Work Step by Step
$r(x)=\frac{2x+6}{-6x+3}$
2x + 6 = 0
x = -3
Thus, the x-intercept is at (-3,0)
y-intercept is the ratio of the constants, which is 6/3 = 2
Thus, the y-intercept is at (0, 2)
Vertical asymptotes are when the denominator is equal to 0
-6x + 3 = 0
x = 1/2
So, domain is from (-∞, 1/2) U (1/2, ∞)
Horizontal asymptote is the ratio of the constants of the leading term (with equal degree)
2/-6 = -1/3
Thus, the horizontal asymptote is at y=-1/3
So the range is from (-∞, -1/3) U (-1/3, ∞)