Answer
x-intercept: (1,0)
y-intercept: None
Vertical Asymptote: x=0, 3
Domain: (-∞, 0) U (0, 3) U (3, ∞)
Horizontal Asymptote: y=0
Range: (-∞, ∞)
See graph below
Work Step by Step
$r(x)=\frac{x^2 - 2x + 1}{(x^3 -3x^2)}$
$x^2 - 2x + 1 = 0$
$(x-1)^2 = 0$
x = 1
x-intercept: (1,0)
No y-intercept as when x=0, the function is undefined
Vertical asymptotes are when the denominator is equal to 0
$x^3 - 3x^2 = 0$
$x^2 (x - 3) = 0$
x = 3, 0
So, domain is from (-∞, 0) U (0, 3) U (3, ∞)
Horizontal asymptote is the ratio of the constants of the leading term (with equal degree)
0 (since leading degree of numerator is lower than leading degree of denominator)
Thus, the horizontal asymptote is at y=0
So the range is from (-∞, ∞)