SOLUTION: y=x-3 Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.

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Question 659376: y=x-3
Test the equation for symmetry with respect to the x-axis, the y-axis, and the origin.


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
y=x-3

1. symmetry about the y-axis
For symmetry about the y-axis, check to see if it is the same when you replace x with -x
-x-3+=+x-3
-1-3+=+1-3
-4+%3C%3E+-2

So y+=+x-3 does NOT have symmetry about the y-axis
2. symmetry about the x-axis
For symmetry about the x-axis, check to see if it is the same when you replace y with -y
-y+=+-x%2B3x-3
So y+=+x-3 does NOT have symmetry about the x-axis
3. diagonal symmetry
For diagonal symmetry, check to see if it is the same when you swap y and x:
x=y-3 ...=>.. is not the same as y=x-3
So y=x-3 does NOT have diagonal symmetry

4. origin symmetry
Start with:
y=x-3

Replace x with -x and y with -y:
-y=-x-3
Multiply both sides by -1:
-y%2A-1=-x%2A%28-1%29-3+%28-1%29
y=x%2B3+
we have the equation y=x%2B3 which is not equal to original equation y=x-3 , hence +y=x-3 does NOT have origin symmetry

+graph%28+600%2C+600%2C+-6%2C+5%2C+-10%2C+10%2C+x-3%29+