Algebraic Test For Symmetry....2

[nycmathguy]

Homework Statement

Use the algebraic tests to check for
symmetry with respect to both axes and the origin.

Relevant Equations

n/a

Use the algebraic tests to check for
symmetry with respect to both axes and the origin.

y = x^4 - x^2 + 3

Let y = - y

-y = x^4 - x^2 + 3

y = (x^4 - x^2 + 3)/-1

y = -x^4 + x^2 - 3

Not symmetric with respect to the x-axis.

Let x = -x

y = (-x)^4 - (-x)^2 + 3

y = x^4 - x^2 + 3

Symmetric with respect to the y-axis.

Let x = -x and y = -y

-y = (-x)^4 - (-x)^2 + 3

y = (x^4 - x^2 + 3)/-1

y = -x^4 + x^2 - 3

Not symmetric with respect to the origin.

 

[fresh_42]

Looks fine.

 

[nycmathguy]

Looks fine.

It feels good to be right.