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 locating 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 locating the lowest point on the graph. Observe the y-coordinate of this point and note the corresponding x-value.
3. Step 3: Write down the maximum value as ƒ(x) = (maximum y-value) and the x-value where it occurs as x = (corresponding x-value).
4. Step 4: Write down the minimum value as ƒ(x) = (minimum y-value) and the x-value where it occurs as x = (corresponding x-value).
5. Step 5: Verify that these points are indeed local extrema by checking the behavior of the graph around these points (the graph should change direction at these points).

Key Concepts

Local Maximum and Minimum

Local maximum and minimum values of a function are points where the function reaches a highest or lowest value in a small neighborhood. These points are important for understanding the behavior of the function and are often found where the slope changes direction.

Reading Graphs to Identify Extrema

To find minimum and maximum values from a graph, observe the highest and lowest points on the curve within the domain. The x-values at these points correspond to where the function attains these extrema, and the y-values give the minimum or maximum function values.

Function Notation and Interpretation

ƒ(x) represents the output value of the function at input x. Understanding this notation helps in interpreting the graph, where the y-axis shows ƒ(x) values and the x-axis shows input values, allowing identification of points where ƒ(x) is minimized or maximized.