Graph Analysis: Creating an Increasing-Decreasing Function Through Two Points

To determine if it is possible to create a function that is both increasing and decreasing using two distinct points, consider these steps:

• Since there are two points, $(x_1, y_1)$ and $(x_2, y_2)$ without specific coordinates mentioned, assume $x_1 \neq x_2$.
• For simplicity, assume the points are arranged such that $x_1 < x_2$.
• Construct a piecewise function around these points. For example:
• If a line joins these two points, identify the slope: $m = \frac{y_2 - y_1}{x_2 - x_1}$.
• This line will either increase (if $m > 0$) or decrease (if $m < 0$).
• To make the function increasing over an interval and decreasing over another, introduce an additional piece at a third point, creating a V or inverse V-shape curve.
• This piecewise approach will make it such that the function increases on one interval and decreases on another, satisfying both conditions.

In conclusion, it is indeed possible to create a function that has increasing and decreasing properties using the two given points by constructing a piecewise function with additional details.

The correct answer to this is: Possible.