1. **State the problem:** We need to evaluate the composite functions \((f \circ g)(4)\) and \((g \circ f)(3)\) using the graphs of \(f(x)\) and \(g(x)\). 2. **Recall the definition of composite functions:** \[(f \circ g)(x) = f(g(x))\] \[(g \circ f)(x) = g(f(x))\] This means we first find the inner function value, then plug it into the outer function. 3. **Evaluate \((f \circ g)(4) = f(g(4))\):** - From the graph, find \(g(4)\). Since \(g(x)\) passes through \((3,1)\) and rises slowly, estimate \(g(4) \approx 1.2\). - Now find \(f(1.2)\). \(f(x)\) is a line through \((0,0)\) and \((5,4)\), so slope \(m = \frac{4-0}{5-0} = \frac{4}{5} = 0.8\). - Equation of \(f(x)\) is \(f(x) = 0.8x\). - Calculate \(f(1.2) = 0.8 \times 1.2 = 0.96\). 4. **Evaluate \((g \circ f)(3) = g(f(3))\):** - Find \(f(3)\) using \(f(x) = 0.8x\): \(f(3) = 0.8 \times 3 = 2.4\). - Find \(g(2.4)\) from the graph. \(g(x)\) passes through \((3,1)\) and \((0,0)\), so estimate \(g(2.4) \approx 0.8\). **Final answers:** \[(f \circ g)(4) \approx 0.96\] \[(g \circ f)(3) \approx 0.8\]