I have 2 problems as stated below:
(a).LeAnn claims that when p(x) and q(x) are polynomials the graph of y = $\left(\frac{p(x)}{q(x)}\right)$ has vertical asymptotes at all the points where q(x) is zero.
If LeAnn is correct, explain why functions of this form will have asymptotes at these points.
If LeAnn is wrong, give an example to show that she is mistaken AND revise her statement so it is correct.
(b) Aaron claims that no matter what the functions f(x) and g(x) are, the graph of $\left(\frac{p(x)}{q(x)}\right)$ has vertical asymptotes at all the points where g(x) is zero and f(x) is not zero.
If Aaron is correct, explain why functions of this form will have these asymptotes.
If Aaron is wrong, give an example to show that he is mistaken AND revise his statement so it is correct.
Since my language is not English I'm not clearly understand these problem. I do know that the vertical asymptotes is = to the root of the denominator where the denominator = 0. So which one of these claim is right and which one is wrong. Please explain. Thanks for the help :)
Hint: Consider $f:\mathbb R\setminus\{0\}\to\mathbb R$ with $f(x) = \frac xx$. What does its graph look like?