Vertical asymptote behavior of (x²-1)/(x²-4) at x = -2

[Glissando]

Homework Statement

Sketch the graphs of the following function showing vertical and horizontal asymptotes and relative extrema:

f(x) = (x²-1)/(x²-4)

Homework Equations

Limits, zeroes, derivatives

The Attempt at a Solution

I know that I have the majority of the answers right, the only problem I'm having is with part of the vertical asymptote.

VA = positive and negative 2

The problem is with -2:

lim (-2²-1)/(-2⁺)²-4)
x->-2⁺

= (4-1)/(4⁺-4) = +infinity

lim ((-2)²-1)/((-2^-)²-4)
x->-2^-

= (4-1)/(4^--4) = negative infinity

But my graphing calculator shows the exact opposite ):!

Any help is appreciated! Thank you <3

 

[Dick]

The limit as x->(-2)+ is +infinity. The limit as x->(-2)- is -infinity. I'm not sure what your graphing calculator's problem is.

 

[Glissando]

The limit as x->(-2)+ is +infinity. The limit as x->(-2)- is -infinity. I'm not sure what your graphing calculator's problem is.

...I guess I'm sketching the graph wrong then...Thank you for your help (:!