Final answer:
The vertical asymptotes for f(x) = (x^3 + 2x^2 - 7)/(x^2 - 4) are x = 2 and x = -2. There is no horizontal asymptote. There are no oblique asymptotes for this function.
Step-by-step explanation:
A vertical asymptote is a vertical line that the graph of a function approaches but never touches. In this case, we can find vertical asymptotes by setting the denominator equal to zero and solving for x. So, x^2 - 4= 0. This equation has two solutions, x = 2 and x = -2. Therefore, the vertical asymptotes for f(x) = (x^3 + 2x^2 - 7)/(x^2 - 4) are x = 2 and x = -2.
A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity. To find horizontal asymptotes, we need to examine the degrees of the numerator and denominator. In this case, the degree of the numerator is 3 and the degree of the denominator is 2. Since the degree of the numerator is greater, there is no horizontal asymptote.
There are no oblique asymptotes for this function.