Math Editor

Deflection Graphs

by Vhince Arjie G. Yarzo

Deflection Graphs refers to graphs or functions that creates a form of deflect relations between the x-axis and a given point.

Functions of Deflection

The functions of deflection prefers functions with a form of "bounce" or any interactions to the x-axis that involves and influences it's path in a line graph. Basically, these are functions playing with mirrored geometry.

For example: We have a function, in which we state that f(x)=px⟹p=1. Now that we have a function, we would test it by graphing:

Notice how the line goes through the origin and is occupying Quadrant I and Quadrant III. Imagine that Quadrant III is a vertically-flipped plane originated from Quadrant II, and observe any more characteristics.

See how the graph seems to deflect when interacting at the x-axis, forming a V-shaped linear graph. This is called a deflection, in which the path of the function interacts with certain conditions and so contribute to moving away from anything related to that circumstance. Non-linear functions mostly hold this interactions.

Now instead of manipulating quadrants to achieve this reaction, what we could use is how to deflect such functions traditionally? We need something that would manipulate the graph's function to achieve the same effect. Nowtice how Quadrant II, having -x but +y, with y = ±x. This illustrates that the y postition is prominently equal to the absolute value of the function. That is right, we use the absolute value function.

f(x)=pxVf(x)=√(px)2​∨∣px∣​

Now, this equation states the evolution of the function, where f(x) is normally seen as f(x) = px. However, if we put a V notation into the function, the function turns into the absolute value of px. This equates the positive integers of negative and positive numbers.

Why use the V notation? (Vhince Notation): The Vhince Notation is a relevant key in studying deflection geometry as it illustrates the dimension of a regular deflective function. In the graph, the line forms a V-shaped path, as of an upside-down triangle, yet we cannot confirm it as a real triangle as the line extends to infinity. Using "V" is showcasing the same function but is in absolute cases would help us identify if the function is absolute (or deflective) or not.

For example: We have a regular linear function

f(x)=−2x+2

If we add the Vhince Notation

Vf(x)=√(−2x+2)2​

If we graph the Vf(x)