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Compare and contrast reflections over the x-axis and y-axis. Generalize your observations

Compare and contrast reflections over the x-axis and y-axis. Generalize your observations

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Compare and contrast reflections over the x-axis and y-axis. Generalize your observations. How does the function behave relative to the location of the negative coefficient? y = − x² vs y = (-x)² or y = √−r vs y VT
Transcribed Image Text:Compare and contrast reflections over the x-axis and y-axis. Generalize your observations. How does the function behave relative to the location of the negative coefficient? y = − x² vs y = (-x)² or y = √−r vs y VT
Expert Solution
Step 1

# As per the guidelines we are entitled to solve one question at a time, please resubmit the other question if you wish to get it answered.

Consider a point (x,y) if the reflection is over x-axis, the x coordinate will remain same and the y co-ordinate will be the additive inverse of the original coordinate.

Therefore, the reflection over x- axis will make the point (x,-y).

It basically will change the side of point over the axis, that is if the point is below the x- axis after reflection it will be up the x- axis, and vice- versa.

Advanced Math homework question answer, step 1, image 1

The original point (5,6) is above the x-axis, after reflection over x- axis it is below the x-axis.

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