f(x)= ⎨x^2-1 / x+1, for x not = -1

⎨8, for x=-1

I'm trying to graph and determine the values of x for which the function is continuous.

Does the graph looks like a u shape opening up or a line.

3 answers

f(x) = (x^2 - 1)/(x+1)
= (x+1)(x-1)/(x+1)
= x-1 , x ≠ -1

so the graph will actually be a straight line
y = x-1 , with a hole at (-1, -2)

the graph will be continuous for all values of x, except x = -1
So the function is defined or not defined.
The question wasn't about a function being defined or not.
You wanted to know if it was continuous.

As I said, it is defined and continuous for all values of x , except x = -1

for all values of x, x ≠-1 , you have the function
f(x) = x-1, which is a straight line
the point (-1,-2) is a hole in the straight line and it is being replaced with (-1,8) , a single point lying above the line.
Strange function.