Question

Determine whether the graph of y^5=x^3 is symmetric with respect to the Y axis the x-axis or the origin.

Answer 1

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Answer:

  the origin

Step-by-step explanation:

Both terms are of odd degree, so the function is an odd function. It is symmetrical with respect to the origin.

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If you recast this as y = f(x), then ...

  f(x) = x^(3/5)

When we look at f(-x), we find ...

  f(-x) = ((-x)^3)^(1/5) = -(x^3)^(1/5) = -(x^(3/5)) = -f(x)

An odd root of a number has the same sign as the number.

When f(-x) = -f(x), the function is odd and symmetrical about the origin.