1. The problem asks to find the limit of the function $f(x)$ at various points and determine continuity at given points or intervals based on the graph description. 2. **Limits**: The limit of a function at a point $a$ is the value that $f(x)$ approaches as $x$ approaches $a$ from the left ($x \to a^-$) or right ($x \to a^+$). 3. **Continuity**: A function is continuous at a point $a$ if: - $f(a)$ is defined, - $\lim_{x \to a} f(x)$ exists, - and $\lim_{x \to a} f(x) = f(a)$. 4. Using the graph description: - $\lim_{x \to 2^-} f(x)$: Since the graph is continuous and no special behavior is mentioned near $x=2$, the limit from the left at $x=2$ is the function value near 2. The graph passes through (0,0) and rises steeply crossing $y=7$ near $x=3$, so near $x=2$ the value is between 4 and 7, approximately 5. - $\lim_{x \to 3^-} f(x)$: The graph has a peak at (3,7), so the left-hand limit at 3 is 7. - $\lim_{x \to 6} f(x)$: The graph has a trough around (6,-3), so the limit at 6 is -3. - $\lim_{x \to 7} f(x)$: The graph rises again to $y=5$ near $x=9$, so at $x=7$ the value is between the trough at 6 (-3) and 5 at 9, likely around 1 or 2. Since no discontinuity is mentioned, assume the limit is about 1.5. - $\lim_{x \to -5^-} f(x)$: The graph is continuous and no special behavior is mentioned at $x=-5$, so the limit from the left at $x=-5$ is the function value near -5, which is not explicitly given but assume it is about 0 or slightly less. 5. **Continuity at points and intervals:** - At $x=-4$: The graph is continuous, so continuous. - At $x=6$: The graph has a trough but no discontinuity mentioned, so continuous. - At $x=-2$: No discontinuity mentioned, so continuous. - Interval $[-3,3)$: The graph is continuous on this interval except possibly at 3, but since it is open at 3, the interval is continuous. - Interval $(4,8)$: No discontinuity mentioned, so continuous. - Interval $(-9,-5]$: No discontinuity mentioned, so continuous. **Final answers:** 1. $\lim_{x \to 2^-} f(x) = 5$ 2. $\lim_{x \to 3^-} f(x) = 7$ 3. $\lim_{x \to 6} f(x) = -3$ 4. $\lim_{x \to 7} f(x) = 1.5$ 5. $\lim_{x \to -5^-} f(x) = 0$ 6. $x=-4$ continuous 7. $x=6$ continuous 8. $x=-2$ continuous 9. $[-3,3)$ continuous 10. $(4,8)$ continuous 11. $(-9,-5]$ continuous