The graph below is the function f(x)
Find lim x -> -1- f(x)=
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As x approaches -1 from the left, the graph of f(x) leads you to the point (-1, 3), so the limit from the left is 3.
As x approaches -1 from the right, the graph leads to the point (-1, -3), so the limit from the right is -3.
The one-sided limits do not match, so the two-sided limit does not exist.
But f(x) is still defined at x = -1; this is indicated by the point (-1, -1). So f (-1) = -1.
We have found all the given limits for all the function.
The limit of a function is a key notion in calculus and analysis that describes how the function behaves near a certain input.
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