1. **State the problem:** We are asked to evaluate limits and function values involving the sum $f(x) + g(x)$ at points $x=1$ and $x=2$ using the given graphs. 2. **Recall limit and function value rules:** - The limit from the left, $\lim_{x \to a^-} f(x)$, is the value $f(x)$ approaches as $x$ approaches $a$ from values less than $a$. - The limit from the right, $\lim_{x \to a^+} f(x)$, is the value $f(x)$ approaches as $x$ approaches $a$ from values greater than $a$. - The function value $f(a)$ is the value of the function at $x=a$. - For sums, $\lim_{x \to a} (f(x) + g(x)) = \lim_{x \to a} f(x) + \lim_{x \to a} g(x)$ if both limits exist. 3. **Evaluate each part:** **a.** $\lim_{x \to 1^-} (f(x) + g(x))$ - From the graph, as $x \to 1^-$, $f(x)$ approaches the filled dot near 2. - As $x \to 1^-$, $g(x)$ approaches the open circle near 0. - Sum: $2 + 0 = 2$ **b.** $\lim_{x \to 1^+} (f(x) + g(x))$ - As $x \to 1^+$, $f(x)$ approaches the open circle near 0. - As $x \to 1^+$, $g(x)$ approaches the filled dot near 4. - Sum: $0 + 4 = 4$ **c.** $f(1) + g(1)$ - $f(1)$ is the value at the filled dot near 2. - $g(1)$ is the value at the filled dot near 4. - Sum: $2 + 4 = 6$ **d.** $\lim_{x \to 2^-} (f(x) + g(x))$ - As $x \to 2^-$, $f(x)$ is near the local max above 3, approximately 3.2. - As $x \to 2^-$, $g(x)$ is decreasing linearly, near 3. - Sum: $3.2 + 3 = 6.2$ **e.** $\lim_{x \to 2^+} (f(x) + g(x))$ - As $x \to 2^+$, $f(x)$ is near 3. - As $x \to 2^+$, $g(x)$ is near 3. - Sum: $3 + 3 = 6$ **f.** $f(2) + g(2)$ - $f(2)$ is the function value at $x=2$, near 3. - $g(2)$ is the function value at $x=2$, near 3. - Sum: $3 + 3 = 6$ **Final answers:** - a. 2 - b. 4 - c. 6 - d. 6.2 - e. 6 - f. 6