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

1 Answer
Feb 13, 2017

Answer:

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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