Find the vertical and horizontal asymptotes of the function \( f(x) = \frac{2x^2 + 3x - 2}{x - 1} \).

Step 1 ：First, we need to find the vertical asymptote. The vertical asymptote of a given function is the x-value that makes the denominator equal to zero. So, we solve the equation \(x - 1 = 0\) which gives us \(x = 1\). Therefore, the vertical asymptote of the function is \(x = 1\).

Step 2 ：Next, we find the horizontal asymptote. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the ratio of the leading coefficients. But in this case, the degree of the numerator (which is 2) is greater than the degree of the denominator (which is 1), so the function does not have a horizontal asymptote. Instead, it has an oblique (slant) asymptote.

Step 3 ：To find the equation of the oblique asymptote, we perform long division of the function \(f(x)\). We divide \(2x^2 + 3x - 2\) by \(x - 1\), which gives us \(2x + 5\). Therefore, the oblique asymptote of the function is \(y = 2x + 5\).