Question

In a couple of sentences and in your own words describe in what ways horizontal, vertical, and oblique asymptotes can be identified.

Answer 1

A horizontal asymptote is one in which y has a limit as x approaches positive or negative infinite. It is usually due to both the denominator and the numerator having the same highest degree term, and the coefficient created by their proportion serves as the asymptote. For example, (2x^2 + 1) / (3x^2) would have a horizontal asymptote of 2/3

A vertical asymptote is an x value at which y approaches infinite. One example includes when the denominator of the function approaches zero at a certain point. For example, (x^2 + 3) / (x + 1) has a vertical asymptote at x=-1, since the denominator approaches zero as x approaches this point. 

For an oblique asymptote, y generally takes the form of a linear function as x approaches infinite. This is the case when the highest term in numerator is one degree higher than the highest degree term in the denominator. 

Examples include (5x^2 + 2) over 2x, where the oblique asymptote is (5/2)x, and even the linear function 2x+3 has an oblique asymptote of 2x