This is an AP question:

> 
> How would you define $f(7)$ in order to make $f$ continuous at $7$?
> 
> 
> $$f(x) = \frac{x^2 - 2x - 3}{x - 7}$$
> 
> 
> 

A long division turns $f$ to

$$f(x) = (x + 5) + \frac{32}{x - 7}.$$

Obviously $f$ tends to infinity at $x = 7$. I don't see how I could define $f(7)$ to make it continuous. Is the question problematic? Any idea?