Key features of polynomial functions analyzed from a graph, including end behavior, intercepts, and extrema.

Looking at the worksheet, I need to analyze two polynomial functions shown in graphs and describe their key features.

Let me start with Problem 1:

Problem 1 Analysis:

The graph shows a polynomial function that:
- Starts from bottom left (as x → -∞, f(x) → -∞)
- Ends going up right (as x → ∞, f(x) → ∞)
- Crosses x-axis at (0,0) and (6,0)
- Has y-intercept at (0,0)
- Has relative minimum at (4,-32)
- Has relative maximum at (0,0)

For end behavior: Since one end goes down and the other goes up, this indicates an odd degree polynomial. The notation "opposite" correctly describes this.

Intercepts are clearly marked as (0,0) and (6,0) for x-intercepts, and (0,0) for y-intercept.

Increasing/decreasing intervals:
- Decreasing on (0,4) - between the max at x=0 and min at x=4
- Increasing on (-∞,0) ∪ (4,∞) - before the max and after the min

Relative extrema:
- Minimum at (4,-32)
- Maximum at (0,0)

Problem 2 Analysis:

The second graph shows:
- End behavior: as x → -∞, g(x) → ∞; as x → ∞, g(x) → -∞ (also opposite, so odd degree)
- X-intercepts appear to be approximately at (-2.6,0), (1,0), and (2.6,0)
- Y-intercept at (0,-4)
- Relative minimum at (-2,-20)
- Relative maximum at (2,12)

Increasing/decreasing:
- Decreasing on (-∞,-2) ∪ (2,∞)
- Increasing on (-2,2)

Both problems have been completed with reasonable accuracy based on visual inspection of the graphs.

Final Answer:
The completed worksheet shows accurate identification of key features for both polynomial functions including end behavior, degree classification, intercepts, increasing/decreasing intervals, and relative extrema points.