Question 213460
your equation is:
{{{f(x) = x^1171 - 5^109 + 3}}}
{{{f(-x) = (-x)^1171 - 5^109 + 3}}}
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{{{x^1171}}} is a positive number we'll call k.
{{{(-x)^1171}}} is a negative number we'll call -k.
example:
(2)^3 = 8
(-2)^3 = -8
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{{{k - 5^109 + 3}}} is not the same as {{{(-k) - 5^109 + 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(x) = x^1171 - 5^109 + 3}}}
solve for -y and -y.
equation becomes:
{{{-y = (-x)^1171 - 5^109 + 3}}}
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before we were able to show that if {{{x^1171 = k}}}, then {{{(-x)^1171 = -k}}}
we use that again to get our equations to become:
{{{y = k - 5^109 + 3}}}
{{{-y = -k - 5^109 + 3}}}
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multiply the second equation by -1 to get:
{{{y = k + 5^109 - 3}}}
this is not the same as:
{{{y = k - 5^109 + 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 = (2x^2 + 5)/7x}}}
replace y with -y and replace x with -x to get:
{{{-y = (2*(-x)^2 + 5)/7(-x)}}}
this becomes:
{{{-y = (2x^2 + 5)/-7x}}}
multiply both sides of this equation by (-1) to get:
{{{y = -(2x^2 + 5) / -7x}}} which becomes:
{{{y = (2x^2 + 5)/7x}}}
the equations are identical when you replace y with -y and you replace x with -x.
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the equation {{{y = (2x^2+5)/7x}}} is symmetric about the origin
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your equation of {{{y = x^1171 - 5^109 + 3}}} is not.
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