1. **State the problem:** We need to find the value of the composition \((f \circ g)(-2)\), which means \(f(g(-2))\). 2. **Identify given functions and values:** - The function \(h(x) = 3x^2 - 4x - 1\) is given but not directly related to \(f\) or \(g\). - The table gives values of \(g(x)\) at specific points: \(g(-2) = 4\). - The graph of \(f(x)\) is a straight increasing line passing through approximately \((0,4)\) and \((6,10)\). 3. **Find \(g(-2)\):** From the table, \(g(-2) = 4\). 4. **Find \(f(4)\):** Since \(f(x)\) is linear and passes through \((0,4)\) and \((6,10)\), find its equation: \[ \text{slope} = \frac{10 - 4}{6 - 0} = \frac{6}{6} = 1 \] Equation of \(f(x)\): \[ f(x) = 1 \cdot x + b \] Using point \((0,4)\): \[ 4 = 0 + b \implies b = 4 \] So, \[ f(x) = x + 4 \] 5. **Evaluate \(f(4)\):** \[ f(4) = 4 + 4 = 8 \] 6. **Final answer:** \[ (f \circ g)(-2) = f(g(-2)) = f(4) = 8 \]