SOLUTION: I have a question that I have been working on and I am wondering if I am on the right path. The question is as follows: Is the graph f(x) = x^1171 - 5^109 + 3 y-axis symmetric, o

Algebra ->  Systems-of-equations -> SOLUTION: I have a question that I have been working on and I am wondering if I am on the right path. The question is as follows: Is the graph f(x) = x^1171 - 5^109 + 3 y-axis symmetric, o      Log On


   

Question 213460: I have a question that I have been working on and I am wondering if I am on the right path. The question is as follows: Is the graph f(x) = x^1171 - 5^109 + 3 y-axis symmetric, origin symmetric, or neither one. Explain your answer.
When working out the problem and replacing x with -x the reworked problem does not come out the same as the original so it is not y-axis symmetric. Then when I multiple (-1) to both sides it does not come out to be the same as the original problem either. So, I am saying that f(x)=x^11171 - 5^109 +3 is neither y-axis or origin symmetric. Am I right with my analysis?
Lori
Found 2 solutions by stanbon, Theo:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The question is as follows: Is the graph f(x) = x^1171 - 5^109 + 3 y-axis symmetric, origin symmetric, or neither one.
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f(-x) = -x^1171 -5^109 + 3 so not symmetric to y axis
-f(-x) = x^1171 + 5^109 - 3 so not symmetric to origin
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You are correct.
Cheers,
Stan H.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your equation is:
f%28x%29+=+x%5E1171+-+5%5E109+%2B+3
f%28-x%29+=+%28-x%29%5E1171+-+5%5E109+%2B+3
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x%5E1171 is a positive number we'll call k.
%28-x%29%5E1171 is a negative number we'll call -k.
example:
(2)^3 = 8
(-2)^3 = -8
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k+-+5%5E109+%2B+3 is not the same as %28-k%29+-+5%5E109+%2B+3 so the equation is not symmetric about the y axis.
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is your equation symmetric about the origin?
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let y+=+f%28x%29+=+x%5E1171+-+5%5E109+%2B+3
solve for -y and -y.
equation becomes:
-y+=+%28-x%29%5E1171+-+5%5E109+%2B+3
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before we were able to show that if x%5E1171+=+k, then %28-x%29%5E1171+=+-k
we use that again to get our equations to become:
y+=+k+-+5%5E109+%2B+3
-y+=+-k+-+5%5E109+%2B+3
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multiply the second equation by -1 to get:
y+=+k+%2B+5%5E109+-+3
this is not the same as:
y+=+k+-+5%5E109+%2B+3
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the equations are not symmetric about the origin either.
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an example of an equation that is symmetric about the origin would be:
y+=+%282x%5E2+%2B+5%29%2F7x
replace y with -y and replace x with -x to get:
-y+=+%282%2A%28-x%29%5E2+%2B+5%29%2F7%28-x%29
this becomes:
-y+=+%282x%5E2+%2B+5%29%2F-7x
multiply both sides of this equation by (-1) to get:
y+=+-%282x%5E2+%2B+5%29+%2F+-7x which becomes:
y+=+%282x%5E2+%2B+5%29%2F7x
the equations are identical when you replace y with -y and you replace x with -x.
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the equation y+=+%282x%5E2%2B5%29%2F7x is symmetric about the origin
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your equation of y+=+x%5E1171+-+5%5E109+%2B+3 is not.
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