Questions: Use the graph of a function y=f(x) to find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values.

Use the graph of a function y=f(x) to find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values.

Transcript text: Use the graph of a function $y=f(x)$ to find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values.

Solution

Solution Steps

Step 1: Identify the Absolute Maximum

The absolute maximum is the highest point on the graph.
From the graph, the highest point is at (5, 3).

Step 2: Identify the Absolute Minimum

The absolute minimum is the lowest point on the graph.
From the graph, the lowest point is at (-1, -4).

Step 3: Identify Local Maximum Values

Local maximum values are the highest points in their immediate vicinity.
From the graph, the local maximum is at (5, 3).

Step 4: Identify Local Minimum Values

Local minimum values are the lowest points in their immediate vicinity.
From the graph, the local minimum is at (3, 0).

Final Answer

Absolute Maximum: (5, 3)
Absolute Minimum: (-1, -4)
Local Maximum: (5, 3)
Local Minimum: (3, 0)

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