The image presents a graph of a trigonometric function plotted on a Cartesian coordinate system, with the x-axis and y-axis labeled. The function appears to be a sine or cosine wave, given its periodic nature and symmetry. **Key Details:** 1. **Axes:** - The horizontal axis is the x-axis. - The vertical axis is the y-axis. 2. **Points:** - The graph passes through several notable points, including: - \((-π, 0)\) - \((-π/2, -1)\) - \((0, 0)\) - \((π/2, 1)\) - \((π, 0)\) 3. **Shape:** - The waveform shows typical characteristics of a sine or cosine function, oscillating between 1 and -1. - It crosses the x-axis at \(-π\), \(0\), and \(π\). - The function reaches a minimum of -1 at \((-π/2, -1)\) and a maximum of 1 at \((π/2, 1)\). **Text Overlay:** Below the graph, the text indicates a question: "Select the correct choice below and fill in any answer boxes within your choice. Use a comma to separate answers as needed." This suggests an interactive component or question related to identifying critical points or analyzing the graph further. ### Using the Given Graph of the Function \( f \), Find the Following: #### (a) Local Maxima - **Problem:** Identify the numbers, if any, at which the function \( f \) has a local maximum. Determine what these local maxima are. #### (b) Local Minima - **Problem:** Identify the numbers, if any, at which the function \( f \) has a local minimum. Determine what these local minima are. --- ### To Solve: #### (a) Finding Local Maxima - **Instructions:** Find the value(s) of \( x \) at which \( f \) has a local maximum. - **Options:** - **A.** \( x = \) (Provide an exact answer, using \(\pi\) as needed.) - **B.** There is no solution. - **Selection:** Choose the correct option for the local maximum from the choices provided. ### Visual Explanation: - There is an implicit reference to a graph of function \( f \) not visible here. To find local maxima or minima, identify points where the function changes direction from increasing to decreasing or vice versa, respectively.