### Quiz 2.5:

Question:

For the function $$f(x)=\frac{x+3}{x^2-3x-10}$$,
(a) At which point(s) is $$f(x)$$ discontinuous and why?
(b) Classify all of your points of discontinuity as removable or not removable and explain why.

Solution:

(a) The function is discontinuous at $$x=,-2,5$$, because those are the zeros of $$x^2-3x-10$$, but not zeros of $$x+3$$ so the function is undefined and has vertical asymptotes at both locations.
(b) Both are not removable because they represent breaks and not holes.