Final answer:
A rational function can have a slant asymptote when the degree of the numerator is one more than the degree of the denominator. The slant asymptote can be found by performing polynomial long division on the function.
Step-by-step explanation:
A rational function can have a slant asymptote when the degree of the numerator is exactly one more than the degree of the denominator. When this condition is met, we can find the slant asymptote by performing polynomial long division on the function. The quotient obtained from the division represents the equation of the slant asymptote.
For example, consider the function f(x) = (x^2 + 2x + 1)/(x + 2). Here, the degree of the numerator is 2 and the degree of the denominator is 1, satisfying the condition. By performing long division, we get a quotient of x + 1, indicating that the slant asymptote is the line y = x + 1.