Question 53515: List the intercepts and test for symmetry.
y = (x^2 - 5)/2x^3 Found 2 solutions by stanbon, venugopalramana:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! List the intercepts and test for symmetry.
y = (x^2 - 5)/2x^3
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Y-intercept:
Let x=0 and you get a meaningless fraction.
So, no Y-intercepts.
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X-intercepts:
Let Y=0.
The fraction is 0 only when the numerator is zero, so:
x^2-5=0
x=sqrt5 or x=-sqrt5
These are the X-intercepts.
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Symmetry:
f(-x)= (x^2-5)/(-2x^3)
-f(-x)= (x^2-5)/(2x^3)
-f(x) does not equal f(x)
Since f(x) does not equal f(-x) there is no y-axis symmetry
Since f(x) does equal -f(-x) there is symmetry to the origin.
Since f(x) does not equal -f(x) there is no x-axis symmetry
Cheers,
Stan H.
You can put this solution on YOUR website! List the intercepts and test for symmetry.
y = (x^2 - 5)/2x^3
at x=0,we have y undefined...tends to infinity..hence the curve goes parallel to y axis approaching it at infinity as x tends to zero
at y=0,we have
x^2=5....x=+sqrt(5) and -sqrt(5) which are the x intercepts.
we find that by replacing x with -x and y with -y,we get same eqn.
-y = {(-x)^2-5}/2(-x)^3
y=(x^2-5)/2x^3 which is same eqn. as the given one.
hence the graph is symmetric about origin
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