Question

Create an original rational function that has at least one asymptote (vertical, horizontal, and/or slant) and possibly a removable discontinuity. List these features of your function: asymptote(s) (vertical, horizontal, slant), removable discontinuity(ies), x-intercept(s), y-intercept, and end behavior.

Answer 1

Since f has a vertical is at x = 2, then the denominator of the rational function contains the term (x - 2). Function f has the form. f(x) = g(x) / (x - 2) g(x) which is in the numerator must be of the same degree as the denominator since f has a horizontal asymptote. Also g(x) must contain the term (x + 5) since f has a zero at x = - 5. Hence f(x) = 3 (x + 5) / (x - 2)