Answer: To find the vertical asymptotes of the given function, we need to find the values of x that make the denominator equal to zero. So, we set each denominator equal to zero and solve for x:
(x-3)(x-1)² = 0
x = 3 or x = 1
Therefore, the vertical asymptotes of the function occur at x = 3 and x = 1.
To find the horizontal asymptotes, we need to look at the degree of the numerator and denominator. Since both the numerator and denominator are degree 2, we can find the horizontal asymptote by dividing the leading coefficient of the numerator by the leading coefficient of the denominator. In this case, the leading coefficient of both the numerator and denominator is 1, so the horizontal asymptote is y = 1/1 = 1.
Therefore, the vertical asymptotes are x = 3 and x = 1, and the horizontal asymptote is y = 1.
Explanation: