Question

How do you determine whether the graph of `absx=-3y` is symmetric with respect to the x axis, y axis or neither?

Answer 1

Symmetric to y-axis;
Not symmetric to x-axis

Explanation:

If a relationship is symmetric to the y-axis then every point `(x,y)` defined by that relationship is reflected through the y-axis as a point `(-x,y)` which is also a member of that relationship.

That is if a relationship is symmetric to the y-axis, we can replace all occurrences of `x` with `(-x)` and the relationship will remain the same.

Given the relationship: `abs(x)=-3y`
since `abs(x)=abs(-x)`
`abs(x)=-3ycolor(white)("XX")`is identical to`color(white)("XX")abs(-x)=-3y`
and the relationship is symmetric to the y-axis

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Similarly, if a a relationship is symmetric to the x-axis, we can replace all occurrences of `y` with `(-y)` and the relationship will remain the same.

Given the relationship: `abs(x)=-3y`
we note that
`abs(x)=-3ycolor(white)("XX")is **not** equivalent to`abs(x)=-3(-y)=+3y#
so the relationship is not symmetric to the x-axis.

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