1. **State the problem:** We are given two functions $f$ and $g$ represented by graphs and asked to evaluate the following composite and combined functions at specific points: - a. $(f+g)(4)$ - b. $(f \circ g)(1)$ - c. \left(\frac{f}{g}\right)(-2)$ - d. $(g \circ f)(3)$ 2. **Recall the definitions:** - $(f+g)(x) = f(x) + g(x)$ - $(f \circ g)(x) = f(g(x))$ - $\left(\frac{f}{g}\right)(x) = \frac{f(x)}{g(x)}$ - $(g \circ f)(x) = g(f(x))$ 3. **Evaluate each part using the graph information:** - a. $(f+g)(4) = f(4) + g(4)$ From the graph, $f(4) = -1$ (since $f$ decreases from $(2,1)$ downwards) and $g(4) = 1$ (since $g$ crosses the x-axis at 4). So, $(f+g)(4) = -1 + 1 = 0$. - b. $(f \circ g)(1) = f(g(1))$ From the graph, $g(1) = 2$ (since $g$ decreases from $y$-intercept 4 to $x$-intercept 4). Then $f(2) = 1$ (given point). So, $(f \circ g)(1) = f(2) = 1$. - c. $\left(\frac{f}{g}\right)(-2) = \frac{f(-2)}{g(-2)}$ From the graph, $f(-2) = 3$ (extrapolating the line upwards) and $g(-2) = 1$ (since $g$ is linear and crosses $y$-axis at 4). So, $\left(\frac{f}{g}\right)(-2) = \frac{3}{1} = 3$. - d. $(g \circ f)(3) = g(f(3))$ From the graph, $f(3) = 0$ (extrapolating line from $(2,1)$ downwards). Then $g(0) = 4$ (the $y$-intercept of $g$). So, $(g \circ f)(3) = g(0) = 4$. 4. **Final answers:** - a. 0 - b. 1 - c. 3 - d. 4 Note: The user provided some answers but the correct evaluation for b is 1, not 7, and for d is 4.