1. **State the problem:** We are given graphs of two functions $f(x)$ and $g(x)$ and asked to evaluate limits and function values involving $f(x)+g(x)$ at specific points. 2. **Recall limit and function value rules:** - The limit of a sum is the sum of the limits, if those limits exist. - The value of $f(x)+g(x)$ at a point is $f(a)+g(a)$ if both functions are defined at $x=a$. - Left-hand limit $\lim_{x \to a^-}$ considers values approaching $a$ from the left. - Right-hand limit $\lim_{x \to a^+}$ considers values approaching $a$ from the right. 3. **Analyze each part:** **a.** As $x \to 1^-$, $f(x) + g(x) \to 2$ (given). **b.** As $x \to 1^+$, $f(x) + g(x) \to 4$ (given). **c.** $f(1) + g(1) = 6$ (given). **d.** As $x \to 2^-$, $f(x) + g(x) \to 6.2$ (given). **e.** As $x \to 2^+$, from the graph: - $f(2^+) \approx 2.9$ - $g(2^+) \approx 4$ Sum: $$2.9 + 4 = 6.9$$ **f.** $f(2) + g(2)$ is the sum of the function values at $x=2$: - $f(2)$ is the value at the filled dot near $3.8$ - $g(2)$ is the value at the filled dot near $2.4$ Sum: $$3.8 + 2.4 = 6.2$$ 4. **Final answers:** - a. 2 - b. 4 - c. 6 - d. 6.2 - e. 6.9 - f. 6.2