Final answer:
The horizontal asymptote is y = 2, and the vertical asymptote is x = -1.
Step-by-step explanation:
To find the horizontal asymptotes of the function r(x) = (2x - 4)/(x^2 + 2x + 1), we need to determine the behavior of the function as x approaches positive infinity and negative infinity. The degree of the numerator and denominator of the function is the same (degree 1), so the ratio of the leading coefficients will determine the horizontal asymptote.
In this case, the ratio is 2/1, which means the horizontal asymptote is y = 2.
To find the vertical asymptotes, we need to set the denominator of the function equal to zero and solve for x. In this case, the denominator is x^2 + 2x + 1, which factors into (x + 1)^2. Hence, the vertical asymptote is x = -1 since the function becomes undefined at that point.