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What is the left hand and right hand limit of 1/x^2 -4 at its vertical asymptote?

Revelant equations

None

Attempt at a solution

It's vertical asymptote are 2 and -2.

I have attached my work . I understand it however at the back of the book it says the left hand limit at 2 is negative infinity. That I don't understand as if you look at the graph I have drawn the left hand limit at 2 is going in a positive direction.

Does anyone have any insight on this? Thank you!