Answer
x-intercept: (2,0)
y-intercept: (0, 2)
Vertical Asymptote: x=4, -1
Domain: (-∞, -1) U (-1, 4) U (4, ∞)
Horizontal Asymptote: y=0
Range: (-∞, ∞)
See graph below
Work Step by Step
$r(x)=\frac{4x - 8}{(x-4)(x+1)}$
$4x - 8 = 0$
x = 2
x-intercept: (2,0)
y-intercept is the ratio of the constants, which is -8 / -4 = 2
Thus, the y-intercept is at (0, 2)
Vertical asymptotes are when the denominator is equal to 0
$(x-4)(x+1) = 0$
x = 4, -1
So, domain is from (-∞, -1) U (-1, 4) U (4, ∞)
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 (-∞, ∞)
