Evaluate the limit as x aproches to -1 of the graphed function

Question

I cant copy an paste the graph but it looks like this

 

is a straight line with an open circle like this "0" and its location is (-1,-2) the line continues going up to the right of the graph and it cross (0,-1) and (1,0).

 

how can i evaluate this limit

Answer 1

If the curve just has a hole in it (the open circle), and the curve approaches the hole from both sides, then the limit is equal to the value that the function would have at that point without the hole.  So, in your case, the limit would = -2.

 

The reason is that as you get closer and closer to the hole (x→ -1) on the x-axis, the y-value gets closer and closer to -2.  At x=-1, the function has no value, but it approaches and gets arbitrarily close to the value of -2.

Answer 2

Daisy,

           What you said indicates that the function that is graphed is not defined at x=-1 i.e. it has no limit there.

Jim