For the function \(f\) graphed below, find the following limits:
1. \(\displaystyle \lim_{x \to -4^{-}}f(x) =\)
2. \(\displaystyle \lim_{x \to -4^{+}}f(x) =\)
3. \(\displaystyle \lim_{x \to -2} f(x) = \)
4. \(\displaystyle \lim_{x \to \infty}f(x) = \)
5. \(\displaystyle \lim_{x \to -\infty}f(x) = \)
1. The limit as we approach -4 from the left = +inf = undefined
2. The limit as we approach -4 from the right = -inf = undefined
3. The limit as we approach -2 from both sides = + inf =undefined
4. The limit as x approaches + inf = -1 (this is the horizontal asymptote )
5. The limit as x approaches - inf = undefined (the function oscillates in this direction )