The graph of a function \( f \) is shown to the right. Use the graph to find the following. \( f(5)=3 \) Choose the correct domain. A. \( (-\infty, \infty) \) B. \( (2,6) \) C. \( (-10,10) \) D. \( (-1,7) \) What is the sel of all x-values such thal \( \mathrm{f}(\mathrm{x})=5 \) ? A. \( \varnothing \) B. \( (-1,7) \) C. \( \{1\} \)

1. We are given from the graph that \[ f(5)=3. \] This information indicates that the graph includes the point \((5,3)\), and the graph’s overall span on the \(x\)-axis covers the interval from \(x=-1\) to \(x=7\). Thus, the domain of \(f\) is the set of all \(x\)-values from \(-1\) to \(7\), which is \[ (-1,\,7). \] Hence, the correct choice for the domain is option D. 2. Next, we want the set of all \(x\) such that \[ f(x)=5. \] From the graph, there is only one point where the output \(y\) equals 5. Reading the graph shows that when \(x=1\), we have \(f(1)=5\). Therefore, the solution set for \(f(x)=5\) is \[ \{1\}. \] Hence, the correct choice for the second question is option C. Final Answers: - Domain: \( (-1,7) \) (choice D) - \( \{x: f(x)=5\} = \{1\} \) (choice C)