Increasing Function Analysis: Connecting Two Fixed Points on a Coordinate Plane

Question

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

000

Video Solution

Solution Steps

00:00 Is it possible to create an increasing function from 2 points?
00:05 Let's look at 3 options
00:10 One option is constant
00:16 The second decreases then increases
00:22 And the third increases then decreases
00:31 Therefore it's impossible to draw an increasing function, and this is the solution to the question

Step-by-Step Solution

To determine whether an increasing function can be created through the given two points, we must analyze and understand what conditions such a function satisfies.

An increasing function means that as xx increases, yy, the function’s value, also increases. In simple terms, if we have two points, (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2), then for the function to be increasing, it must be that x1<x2x_1 < x_2 and y1<y2y_1 < y_2.

Starting from this understanding, observe the provided points. Assuming coordinates are (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) with specifics determined visually or contextually:

  • Verify that both points have distinct xx-coordinates such that x1<x2x_1 < x_2.
  • Check and confirm whether their respective yy-coordinates are such that y1<y2y_1 < y_2.

Upon observing plot arrangements, while the horizontal axis marks a left-right progression, the vertical arrangement negates: if corresponding plot layers detected inversely, no increase in height is shown relative to positional depth.

Therefore, observe if x1<x2x_1 < x_2 but y1>y2y_1 > y_2, causing the conclusion that such positional arrangement doesn't naturally derive an increasing function.

Conclusively, since this presented pattern arguably displays a decreasing nature, a true increasing function based on arrangement interpretation from two points is No.

Answer

No