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

Key Concepts

Maximum and Minimum Values

In the context of a function, the maximum value is the highest point on the graph, while the minimum value is the lowest point. These values are crucial for understanding the behavior of the function, as they indicate the range of outputs the function can produce. In the provided graph, the maximum value is 9, and the minimum value is 1.

X-Values at Extrema

The x-values at which the maximum and minimum values occur are the points on the x-axis corresponding to these extrema. Identifying these x-values is essential for understanding the function's behavior at specific points. In the graph, the maximum occurs at a certain x-value, and the minimum occurs at another, which can be determined by observing the graph.

Graph Interpretation

Interpreting a graph involves analyzing its shape, peaks, and valleys to extract meaningful information about the function it represents. This skill is vital in college algebra, as it allows students to visualize and understand the relationships between variables. The provided graph shows clear peaks and troughs, making it easier to identify the maximum and minimum values and their corresponding x-values.