Is it possible to create an increasing function with the two given points?
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Is it possible to create an increasing function with the two given points?
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 increases, , the function’s value, also increases. In simple terms, if we have two points, and , then for the function to be increasing, it must be that and .
Starting from this understanding, observe the provided points. Assuming coordinates are and with specifics determined visually or contextually:
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 but , 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.
No
Does the function in the graph decrease throughout?
A function is increasing when moving from left to right, the function values (y-coordinates) get larger. If , then we need .
Yes! If the slope between two points is positive, the function is increasing between those points. If the slope is negative, it's decreasing.
If both points have the same y-value, the function is constant (neither increasing nor decreasing) between those points. The slope would be zero.
This specific rule applies to any function between two points! Whether the actual function is a line, curve, or step function, if it's increasing, the right point must be higher than the left point.
Look for grid lines and count carefully from the origin (0,0). The first number is the x-coordinate (horizontal), and the second is the y-coordinate (vertical).
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