For each function graphed, give the minimum and maximum values of ƒ(x) and the x-values at which they occur.

Verified step by step guidance

1. Step 1: Identify the maximum value of the function by looking for the highest point on the graph. This is where the function reaches its greatest y-value.
2. Step 2: Note the x-coordinate corresponding to this maximum y-value. This gives the location where the maximum occurs.
3. Step 3: Identify the minimum value of the function by finding the lowest point on the graph. This is where the function reaches its smallest y-value.
4. Step 4: Note the x-coordinate corresponding to this minimum y-value. This gives the location where the minimum occurs.
5. Step 5: Summarize the results by stating the maximum value and its x-coordinate, and the minimum value and its x-coordinate.

Key Concepts

Maximum and Minimum Values of a Function

Maximum and minimum values of a function are the highest and lowest points on its graph, respectively. The maximum value is the largest y-value the function attains, while the minimum is the smallest y-value. These points can occur at specific x-values and are important for understanding the function's range.

Reading Coordinates from a Graph

To find maximum and minimum values, you must accurately read the coordinates of key points on the graph. The x-coordinate indicates where the extremum occurs, and the y-coordinate gives the function's value at that point. This skill is essential for interpreting graphical data.

Piecewise Linear Functions

The graph shown is a piecewise linear function, composed of straight line segments. Understanding how to analyze such functions involves identifying points where the slope changes, which often correspond to local maxima or minima. This helps in determining the function's behavior over different intervals.