Question

HELP WITH CALCULUS!

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. Provide any other details that would enable another student to graph and determine the equation for your function. Do not state your function.

Answer 1

This function has a hole at x = -3 (point: (-3, -1/6) which is removable)
This function has a vertical asymptote x = 3
This function has a horizontal asymptote y = 0 (degree of numerator < degree of denominator)
It has no x - intercept
Its' y - intercept is at (0, -1/3)
As x →-∞, f(x) →0 and as x →∞, f(x) →0

The function is
`f(x)= (x+3)/((x+3)(x-3))`