1. **State the problem:** We need to find the limit $$\lim_{x \to -3} (f(x) + h(x))$$ where functions $f$ and $h$ are given graphically. 2. **Recall the limit sum rule:** The limit of a sum is the sum of the limits, if both limits exist: $$\lim_{x \to a} (f(x) + h(x)) = \lim_{x \to a} f(x) + \lim_{x \to a} h(x)$$ 3. **Find $$\lim_{x \to -3} f(x)$$:** - From the graph description, $f$ has a jump at $x = -3$. - The left-hand limit as $x \to -3^-$ is the value approaching from the left segment ending at an open circle at $(-3,3)$, so $$\lim_{x \to -3^-} f(x) = 3$$. - The right-hand limit as $x \to -3^+$ is the value starting at an open circle at $(-3,0)$, so $$\lim_{x \to -3^+} f(x) = 0$$. - Since left and right limits differ, $$\lim_{x \to -3} f(x)$$ does not exist. 4. **Find $$\lim_{x \to -3} h(x)$$:** - The graph of $h$ is continuous and passes through $(-3,2)$. - Both left and right limits at $x = -3$ are 2, so $$\lim_{x \to -3} h(x) = 2$$. 5. **Evaluate the sum limit:** - Since $$\lim_{x \to -3} f(x)$$ does not exist, the sum limit $$\lim_{x \to -3} (f(x) + h(x))$$ does not exist. **Final answer:** The limit does not exist. **Answer choice:** E