Question 53515
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.