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 [math]lim_{x\to0}f\left(x\right)[/math] exists
Let [math]a,b\in\mathbb{R}[/math], give an example of a function with asymptotes at [math]-a[/math] and [math]b[/math].
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.