The graph above represents the function $f(x)$ based on the given conditions:

• $f(-2) = 0$, with limits:

  • $\lim_{x \to -2^-} f(x) = 4$
  • $\lim_{x \to -2^+} f(x) = 0$
  • $\lim_{x \to -2} f(x)$ does not exist due to a jump discontinuity at $x = -2$.

• $f(-4) = 4$, with limits:

  • $\lim_{x \to -4^-} f(x) = 4$
  • $\lim_{x \to -4^+} f(x) = 4$
  • $\lim_{x \to -4} f(x) = 4$, indicating a continuous point at $x = -4$.

Do you have any questions or need further details?

Here are 5 related questions:

1. What is the definition of a jump discontinuity?
2. How do left-hand and right-hand limits differ at a discontinuity?
3. What does it mean when a limit does not exist at a point?
4. How does continuity affect the existence of limits?
5. Can a function be discontinuous but still have limits on both sides of a point?

Tip: When evaluating limits, always check the left-hand and right-hand behavior of the function at the point of interest.