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Question 443325: This is a long question with multiple parts but is just one single question my professor gave me to work on but that I'm stuck on.
Test: 1. y=x to the 4th minus 2x squared
2. y=x to the 3rd minus 6x
3. y=x squared + 2x + 1
for symmetry with respect to:
1. x-axis
2. y-axis
3. the origin (0,0)
4. write them in function notation and say which one is even, odd, or neither?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 1. y=x to the 4th minus 2x squared
2. y=x to the 3rd minus 6x
3. y=x squared + 2x + 1
for symmetry with respect to:
1. x-axis
2. y-axis
3. the origin (0,0)
4. write them in function notation and say which one is even, odd, or neither?
--------------------------------------------------------------------------------I. y=x to the 4th minus 2x squared
f(x) = x^4-2x^2
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1. Check f(x) = -f(x)
x^4-2x^2 = -(x^4-2x^2)
Ans: no x-axis symmetry
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2. Check f(x) = f(-x)
x^4-2x^2 = (-x)^4-2(-x^2)
x^4-2x^2 = x^4-2x^2
Ans: yes so y-axis symmetry
--------------------------
3rd: Check f(x) = -f(-x)
x^4-2x^2 = -((-x)^4-2(-x)^2)
x^4-2x2 = -(x^4-2x^2)
Ans: no so no origin symmetry
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Do the same for the other listed problems.
Form f(x), -f(x), f(-x) and -f(-x)
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If f(x) = -f(-x) you have x-axis symmetry
If f(x) = f(-x) you have y-axis symmetry
If f(x) = -f(-x) you have origin symmetry
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Cheers,
Stan H.
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