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.
Thank you in advance :)

Answer 1

Since f has a vertical 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)