The function f(x)=(x^2-4)/(x-1) has the following asymptotes. (You can choose more than one). a) Vertical asymptote b) Horizontal asymptote c) Oblique asymptote

## Step 1: Finding Vertical Asymptotes<br />### Vertical asymptotes occur where the denominator is zero and the numerator is non-zero. We set the denominator equal to zero: $x - 1 = 0$, which gives $x = 1$. Since the numerator $x^2 - 4$ is not zero at $x=1$, there is a vertical asymptote at $x=1$.<br /><br />## Step 2: Finding Horizontal Asymptotes<br />### Horizontal asymptotes exist when the degree of the numerator is less than or equal to the degree of the denominator. Here, the degree of the numerator ($x^2 - 4$) is 2, and the degree of the denominator ($x - 1$) is 1. Since the degree of the numerator is greater than the degree of the denominator, there are no horizontal asymptotes.<br /><br />## Step 3: Finding Oblique Asymptotes<br />### Oblique asymptotes occur when the degree of the numerator is exactly one greater than the degree of the denominator. In this case, the degree of the numerator (2) is exactly one greater than the degree of the denominator (1). We perform polynomial long division to find the oblique asymptote: $\frac{x^2 - 4}{x - 1} = x + 1 - \frac{3}{x - 1}$. As $x$ approaches infinity, the term $\frac{-3}{x-1}$ approaches 0. Therefore, the oblique asymptote is $y = x + 1$.