f(x) = 2x^3 + x is an odd function
Reasoning:
We need to show that f(-x) = -f(x) for all x in the domain.
f(x) = 2x^3 + x
f(-x) = 2(-x)^3 + (-x)
f(-x) = -2x^3 - x
f(-x) = -( 2x^3 + x )
f(-x) = -f(x)
We have shown that f(x) = 2x^3 + x is an odd function
Take note how 2x^3+x is the same as 2x^3+x^1, in which all of the exponents are odd numbers.
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The parabola shown is neither even nor odd
Reason: There isn't symmetry along the y axis, which means the parabola is not even. It's not odd either because we don't have symmetry about the origin. Furthermore, the parabola does not go through the origin. All odd functions must pass through the origin.
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The other parts of the question are obscured, so it's impossible to answer those.