Question

f(x) = {x^2-x / (x+1) if x does not = -1
{ 0 if x = -1

Is this graph continuous at x = -1? Please explain! Thanks

Answer 1

if x = -1 then what is f(-1)?

Answer 2

remember the definition: f is continous at x=-1 if
\[ \large \lim_{x\to-1}f(x)=f(-1) \]

Answer 3

this is not as hard as it looks
replace \(x\) by -1 in the expression \(\frac{x^2-x}{x+1}\)
you will get \(\frac{2}{0}\) which is undefined
so forget about it being continuous at -1\
if you got \(\frac{0}{0}\) you would have more work to do, but in this case there is nothing to compute after that