Describe how the values of \( y \) behave to result in a maximum or minimum value. As the values of \( x \) increase across the domain of a function, a maximum value occurs when the \( y \)-values change from [Select ] [Select] As the value of \( x \) increases across the domain of a function, a minimum value occurs when th \( y \)-values change from [Select] [Select ]

When analyzing the behavior of a function to determine where it reaches maximum or minimum values, it's essential to observe how the \( y \)-values change as \( x \) increases across the domain. 1. **Maximum Value:** - **Behavior:** A maximum value occurs at a point where the function changes its trend from increasing to decreasing. - **Explanation:** As \( x \) increases, the \( y \)-values of the function are getting larger (increasing). When the function reaches a peak, the \( y \)-values stop increasing and begin to decrease. This transition from increasing to decreasing indicates a **maximum** point. **Completion:** - The \( y \)-values change from **increasing** to **decreasing**. 2. **Minimum Value:** - **Behavior:** A minimum value occurs at a point where the function changes its trend from decreasing to increasing. - **Explanation:** As \( x \) increases, the \( y \)-values of the function are getting smaller (decreasing). When the function reaches the lowest point, the \( y \)-values stop decreasing and begin to increase. This transition from decreasing to increasing indicates a **minimum** point. **Completion:** - The \( y \)-values change from **decreasing** to **increasing**. **Summary:** - **Maximum:** \( y \)-values change from **increasing** to **decreasing**. - **Minimum:** \( y \)-values change from **decreasing** to **increasing**. This behavior typically corresponds to critical points in the function where the first derivative is zero, indicating potential maxima or minima. **Visual Representation:**  *In the graph above, the peak represents a maximum where the function transitions from increasing to decreasing, and the trough represents a minimum where it transitions from decreasing to increasing.* --- **Key Takeaways:** - **Maximum Point:** Transition from increasing to decreasing. - **Minimum Point:** Transition from decreasing to increasing. Answer Summary: • A maximum occurs where y changes from increasing to decreasing. • A minimum occurs where y changes from decreasing to increasing.