Answer
x-intercept: None
y-intercept: (0, 5/4)
Vertical Asymptote: x=-2
Domain: (-∞, -2) U (-2, ∞)
Horizontal Asymptote: y=5
Range: [1, ∞)
See graph below
Work Step by Step
$r(x)=\frac{5x^2 + 5}{(x^2 + 4x + 4)}$
No x-int as the numerator will never equal 0
y-intercept is the ratio of the constants, which is 5/4
Thus, the y-intercept is at (0, 5/4)
Vertical asymptotes are when the denominator is equal to 0
$x^2 + 4x +4 = 0$
$(x+2)^2 = 0$
x = -2
So, domain is from (-∞, -2)U (-2, ∞)
Horizontal asymptote is the ratio of the constants of the leading term (with equal degree)
5/1 = 5
Thus, the horizontal asymptote is at y=5
So the range is from [1, ∞) (according to the graph)