Determine whether the function is even, odd, or neither.
$f ( x ) = x ^ { 2 } ( 3 - x ) ^ { 2 }$
A) odd
B) even
C) neither

Question

Determine whether the function is even, odd, or neither. 
$f ( x ) = x ^ { 2 } ( 3 - x ) ^ { 2 }$
A) odd
B) even
C) neither

Quizplus · Accepted Answer

To check if a function is even, we substitute -x for x and simplify. If the function remains unchanged, it is even. To check if a function is odd, we substitute -x for x, simplify and then multiply by -1. If the resulting function is the same as the original function, it is odd. 
In this case, substituting -x for x gives us:
$f(-x) = (-x)^2(3-(-x))^2 = x^2(3+x)^2$
Multiplying by -1 gives us:
$-f(x) = -x^2(3-x)^2$
These two functions are not the same, therefore the given function is neither even nor odd.

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

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