Determine whether the given function is even, odd, or neither.
-$$f ( x ) = x ^ { 3 } + x ^ { 2 } - 5$$
A) Neither
B) Even
C) Odd Use possible symmetry to determine whether the graph is the graph of an even function, an odd function, or a function that is neither even nor odd.

Question

Quizplus · Accepted Answer

A function is even if $ f(-x) = f(x) $ and odd if $ f(-x) = -f(x) $. For $ f(x) = x^3 + x^2 - 5 $, $ f(-x) = (-x)^3 + (-x)^2 - 5 = -x^3 + x^2 - 5 $. Since $ f(-x) \neq f(x) $ and $ f(-x) \neq -f(x) $, the function is neither even nor odd.

Determine Whether the Given Function Is Even, Odd, or Neither f(x)=x3+x2−5f ( x ) = x ^ { 3 } + x ^ { 2 } - 5f(x)=x3+x2−5

Determine Whether the Given Function Is Even, Odd, or Neither $f ( x ) = x ^ { 3 } + x ^ { 2 } - 5$