Creating an Increasing Function: Do Points (x1, y1) and (x2, y2) Qualify?

Is it possible to create an increasing function with the two given points?

Given two points $A$ and $B$ on a plane, we need to determine if a function can pass through these points such that it is increasing.

Consider the definition of an increasing function: For the function to be increasing, if $x_2 > x_1$, then it must satisfy $y_2 > y_1$.

Let's apply this to the problem:

• Let the first point be $A = (x_1, y_1)$ and the second point be $B = (x_2, y_2)$.
• The function is increasing between these two points if $x_2 > x_1$ and $y_2 > y_1$.

From the information provided, since the graph indicates that the point corresponding to $B$ is vertically above $A$, it follows that:

• The $x$-coordinates are ordered such that $x_2 > x_1$.
• The $y$-coordinates satisfy $y_2 > y_1$.

Both necessary conditions hold, so it is indeed possible to create an increasing function passing through these two points.

Therefore, the answer to the problem is Yes.