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. Observe the y-coordinate of this point and note the corresponding x-value.
2. Step 2: Identify the minimum value of the function by looking for the lowest point on the graph. Observe the y-coordinate of this point and note the corresponding x-value.
3. Step 3: From the graph, the maximum value occurs at the highest peak, which is at y = 9. Find the x-value where this maximum occurs by tracing down to the x-axis.
4. Step 4: Similarly, the minimum value occurs at the lowest point, which is at y = 1. Find the x-value where this minimum occurs by tracing down to the x-axis.
5. Step 5: Summarize the results by stating the minimum and maximum values of ƒ(x) along with their corresponding x-values.

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 output (y-value) the function attains, while the minimum is the smallest. These values can occur at specific x-values, which are important for understanding the function's behavior.

Reading and Interpreting Graphs

Interpreting graphs involves identifying key points such as peaks (maxima) and valleys (minima) by analyzing the plotted curve. Understanding the scale and axes helps determine the exact coordinates of these points, which represent the function's output values at given inputs.

Coordinate Plane and Function Notation

The coordinate plane uses x (horizontal) and y (vertical) axes to plot points representing function values. Function notation ƒ(x) denotes the output y for an input x. Recognizing how to read these coordinates is essential for identifying where the function reaches its minimum and maximum.