Let's analyze the two graphs in the image and extract the necessary information about relative maximum, relative minimum, and the intervals where the functions are increasing or decreasing.

Graph 1:

• Relative Max: The graph has a relative maximum at the point $x = 0$, with a maximum value of approximately 6.
• Relative Min: The graph has a relative minimum at the point $x = 4$, with a minimum value of approximately 0.
• Increasing Intervals: The function is increasing for $x < 0$ (left of the maximum), specifically from $(-\infty, 0)$.
• Decreasing Intervals: The function is decreasing for $0 < x < 4$ (between the maximum and minimum), specifically from $(0, 4)$. After $x = 4$, it appears to start increasing again slightly.

Graph 2:

• Relative Max: There does not seem to be a clear relative maximum; the function appears to keep increasing.
• Relative Min: The graph has a relative minimum at $x = 2$, with a minimum value of approximately 0.
• Increasing Intervals: The function is increasing for $x > 2$ (to the right of the minimum), specifically from $(2, \infty)$.
• Decreasing Intervals: The function is decreasing for $x < 2$ (to the left of the minimum), specifically from $(-\infty, 2)$.

Would you like more details on any specific part of this analysis?

Follow-up questions:

1. What does the first derivative of each function tell us about these intervals?
2. How would the second derivative help in identifying concavity and points of inflection for these graphs?
3. How do these graphs represent continuous and discontinuous behavior in functions?
4. How would a vertical asymptote affect the increasing/decreasing nature of a function?
5. Can you use these graphs to approximate the roots (zeros) of each function?

Tip: Always check for symmetry in graphs to identify whether a function has certain characteristics like being even, odd, or neither. This can simplify analysis.