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.
