Let's work through the answers.

For part a (a = 0):

1. $\lim_{x \to 0^-} f(x)$ (left-hand limit as $x$ approaches 0):

   • From the graph, as $x$ approaches 0 from the left, $f(x)$ tends toward 2.

2. $\lim_{x \to 0^+} f(x)$ (right-hand limit as $x$ approaches 0):

   • As $x$ approaches 0 from the right, $f(x)$ also tends toward 2.

3. $\lim_{x \to 0} f(x)$ (two-sided limit as $x$ approaches 0):

   • Since both left and right limits are equal, the limit as $x$ approaches 0 is 2.

4. $f(0)$ (value of the function at $x = 0$):

   • The graph shows that $f(0) = 2$.

For part b (a = 2):

1. $\lim_{x \to 2^-} f(x)$ (left-hand limit as $x$ approaches 2):

   • As $x$ approaches 2 from the left, $f(x)$ approaches -2.

2. $\lim_{x \to 2^+} f(x)$ (right-hand limit as $x$ approaches 2):

   • As $x$ approaches 2 from the right, $f(x)$ tends toward 2.

3. $\lim_{x \to 2} f(x)$ (two-sided limit as $x$ approaches 2):

   • Since the left and right limits are not equal, the two-sided limit does not exist.

4. $f(2)$ (value of the function at $x = 2$):

   • The graph shows $f(2) = 0$ (solid point at $x = 2$).

Let me know if you want further details!