Question

Which phrase best describes f(x), graphed on the coordinate plane below? f(x) is an odd function. f(x) is an even function. f(x) is both odd and even. f(x) is neither odd nor even.

Answer 1

if
$f(x) = f( - x) \\ \\ f(x) \: is \: a \: even \: function$
also the graph is symmetrical abt y axis.

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if
$f( - x) = - f(x) \\ f(x) \: is \: odd \: function \: and \: graph \: is \: symm \: about \: origin \\ \\ for \: eg \: \\ f(x) = {x}^{3} \\ f( - x) = - {x}^{3} \\ f( - x) = - f(x)$

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if
$f( - x) \: is \: neither \: f(x) \: nor \: - f(x) \\ \\ then \: f(x) \: is \: neither \: odd \: nor \: even \\ \\ example \\ f(x) = {e}^{x}$

Answer 2

A)  f(x) is an odd function.