Question

directions: identify the extrema and end - behavior of each of the four functions
1)

• relative maxima:
• relative minima:
• absolute minimum:
• absolute maximum:
• describe the end - behavior:

2)

• relative maxima:
• relative minima:
• absolute minimum:
• absolute maximum:
• describe the end - behavior:

3)
relative maxima:
relative minima:
absolute minimum:
absolute maximum:
describe the end - behavior:
4)

• relative maxima:
• relative minima:
• absolute minimum:
• absolute maximum:
• describe the end - behavior:

Explanation:

Step1: Identify relative extrema

Relative maxima are points where the function changes from increasing to decreasing, and relative minima are points where the function changes from decreasing to increasing. Observe the peaks and valleys of the function graphs.

Step2: Determine absolute extrema

The absolute minimum is the lowest - point on the entire graph, and the absolute maximum is the highest - point on the entire graph. Consider the range of the function over its entire domain shown in the graph.

Step3: Analyze end - behavior

Describe what happens to the function as \(x\to+\infty\) and \(x\to-\infty\). If the graph goes up on both ends, we say as \(x\to\pm\infty\), \(y\to+\infty\); if it goes down on both ends, as \(x\to\pm\infty\), \(y\to-\infty\); if one end goes up and the other goes down, we describe them separately.

Since the graphs are not clear enough to give specific coordinates:

Answer:

For each function:

1. Relative Maxima: Coordinates of points where the function changes from increasing to decreasing.
2. Relative Minima: Coordinates of points where the function changes from decreasing to increasing.
3. Absolute Minimum: Coordinate of the lowest - point on the entire graph.
4. Absolute Maximum: Coordinate of the highest - point on the entire graph.
5. End - Behavior: Describe what the function does as \(x\to+\infty\) and \(x\to-\infty\) (e.g., \(y\to+\infty\) as \(x\to+\infty\) and \(y\to-\infty\) as \(x\to-\infty\)).