Determine if the function is even, odd, or neither.
-$f ( x ) = 0.5 x ^ { 2 } + | x | + 3$
A) Odd
B) Even
C) Neither

Name: Determine if the function is even, odd, or neither. -$f ( x ) = 0.5 x ^ { 2 } + | x | + 3$ A) Odd B) Even C) Neither
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Question

Quizplus · Accepted Answer

An even function satisfies $f(-x) = f(x)$ for all $x$ in its domain. For $f(x) = 0.5x^2 + |x| + 3$, replacing $x$ with $-x$ gives $0.5(-x)^2 + |-x| + 3 = 0.5x^2 + |x| + 3$, which is the same as the original function. Thus, $f(x)$ is even.

Determine If the Function Is Even, Odd, or Neither f(x)=0.5x2+∣x∣+3f ( x ) = 0.5 x ^ { 2 } + | x | + 3f(x)=0.5x2+∣x∣+3

Determine If the Function Is Even, Odd, or Neither $f ( x ) = 0.5 x ^ { 2 } + | x | + 3$