Friday, October 30, 2020

Symmetry with respect to each axis and to the origin

By Nhat Nguyen at 7:53 AM    No comments
Problem Solution
y = x^2 - 6
Symmetric with respect to the y-axis because:
y=(-x)^2 - 6= x^2 - 6
y = x^2 - x no symmetry with respect to either axis or the origin
No symmetry with respect to either axis or the origin
y^2 = x^3 - 8x

Symmetric with respect to the x-axis because:
(-y)^2 = y^2 = x^3 - 8x symmetric with respect to the x-axis
y = x^3 + x
Symmetric with respect to the origin because:
(-y) = (-x)^3 + (-x)
(-y) = -x^3 - x
-y = x^3 + x
xy = 4

Symmetric with respect to the origin because:
(-x) (-y) = xy = 4
xy^2 = -10

Symmetric with respect to the origin because:
x(-y)^2 = xy^2 = -10
y = 4 - sqrt(x + 3 no symmetry with respect to either axis or the origin
No symmetry with respect to either axis or the origin
xy - sqrt(4 - x^2) = 0
 Symmetric with respect to the origin because:

symmetric with respect to the origin because xy - sqrt(4 - x^2) = 0
y = x/(x^2 + 1)
Symmetric with respect to the origin because:

symmetric with respect to the origin because -y = -x/(-x)^2 + 1

symmetric with respect to the origin because y = x/(x^2 + 1)
y = (x^2) / (x^2 + 1)

y = (x^2)/(x^2 + 1) is symmetric with respect to the y-axis because

is symmetric with respect to the y-axis because 

y = ((-x)^2))/((-x)^2 + 1) = (x^2)/(x^2 + 1)
y = |x^3 + x|

y = |x^3 + x| is symmetric with respect to the y-axis because

is symmetric with respect to the y-axis because

y = |(-x)^3 + (-x)|=|-(x^3 + x)| = |x^3 + x

y = |(-x)^3 + (-x)|=|-(x^3 + x)| = |x^3 + x
|y| - x = 3

|y| - x = 3 is symmetric with respect to the x-axis because

is symmetric with respect to the x-axis because

|-y| - x = 3

|y| - x = 3

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