Questions on asymptotes

Using your knowledge of functions, limits and asymptotes, anwer the following questions. You can use the applet below to visualise functions and check your answers.

Give an example of a function with vertical asymptote at x=3

Give an example of a function f(x) with vertical asymptote at x=0, and exists

Let , give an example of a function with asymptotes at and .

Give a counter-example to the claim that trigonometric functions do not have vertical asymptotes.

Give a counter example to the claim that all functions only have horizontal asymptotes at y=0.