**Graph Analysis and Function Behavior** **Question 4** Find the open intervals on which the function is increasing and decreasing. Identify the function's local and absolute maximum and minimum values. **Graph Description:** The graph provided portrays a function with its behavior plotted on a Cartesian plane, showing changes in direction on the y-axis as x values change: - The x-axis is labeled from -5 to 5. - The y-axis ranges from 0 to at least 7. - The function appears to have a parabolic shape downward opening with an intersection at the y-axis, and then it sharply increases, indicating a change in behavior. **Options for Identifying Function Behavior:** - **Option A:** - Increasing on (-2, 0) and (2, 4); decreasing on (0, 2) - Absolute maximum at (4, 7); local maximum at (0, 2); absolute minimum at (-2, 0) and (2, 0) - **Option B:** - Increasing on (-2, 0) and (2, 4); decreasing on (0, 2) - Absolute maximum at (4, 7) and (0,2); absolute minimum at (-2, 0) and (2, 0) - **Option C:** - Increasing on (-2, 0) and (2, 4); decreasing on (0, 2) - Absolute maximum at (4, 7); absolute minimum at (-2, 0) and (2, 0) - **Option D:** - Increasing on (2, 4); decreasing on (0, 2) - Absolute maximum at (4, 7); local maximum at (0, 2); absolute minimum at (-2, 0) and (2, 0) **Approach:** Examine the graph to determine where the function is rising or falling, and locate points of highest and lowest values along these intervals to select the correct description. **Question 4** Find the open intervals on which the function is increasing and decreasing. Identify the function's local maximum and minimum points. **Graph Description:** The graph shows a function plotted on a coordinate plane with the x-axis ranging from -5 to 5 and the y-axis from -1 to 8. The curve of the function appears to be a cubic-like shape with critical points: - A local minimum near \((-2, 0)\) - A local maximum near \((0, 2)\) - Another local minimum near \((2, 0)\) - Rising steeply after \((2, 0)\) **Options:** - A) Increasing on \((-2, 0)\) and \((2, 4)\); decreasing on \((0, 2)\); Absolute maximum at \((4, 7)\); local maximum at \((0, 2)\); absolute minimum at \((-2, 0)\) and \((2, 0)\) - B) Increasing on \((-2, 0)\) and \((2, 4)\); decreasing on \((0, 2)\); Absolute maximum at \((4, 7)\) and \((0, 2)\); absolute minimum at \((-2, 0)\) and \((2, 0)\) - C) Increasing on \((-2, 0)\) and \((2, 4)\); decreasing on \((0, 2)\); Absolute maximum at \((4, 7)\); absolute minimum at \((-2, 0)\) and \((2, 0)\) - D) Increasing on \((2, 4)\); decreasing on \((0, 2)\); Absolute maximum at \((4, 7)\); local maximum at \((0, 2)\); absolute minimum at \((-2, 0)\) and \((2, 0)\) **Note:** Selecting an option and moving to another question will save the response.