From the image, the problem asks to find the following limits and function values using the provided graph for each given value of $a$.

We are asked to evaluate the limits as $x \to a$ from both the left and right, as well as the function value at $x = a$, for two cases: $a = 0$ and $a = 2$.

Let’s focus on part a.i for $a = 0$:

The question asks for: $\lim_{x \to 0^-} f(x)$ This represents the left-hand limit as $x$ approaches 0 from the left side (negative direction).

Examining the graph at $a = 0$:

• For $x \to 0^-$ (left of 0), the function values are approaching 6 based on the direction of the arrow from the left side.

Thus, the limit is: $\lim_{x \to 0^-} f(x) = 6$

Would you like to proceed with solving the other limits or ask more questions?

Here are 5 related questions:

1. What is the right-hand limit $\lim_{x \to 0^+} f(x)$?
2. Does $\lim_{x \to 0} f(x)$ exist, and why?
3. What is $f(0)$, the actual function value at $x = 0$?
4. What happens when $a = 2$ for the same limits and function value?
5. How can you determine when a limit does not exist from a graph?

Tip: When evaluating limits, always check for continuity by comparing the left-hand and right-hand limits. If they differ, the limit at that point does not exist.