Determine if the function is even, odd, or neither.
-$f ( x ) = 0.25 x ^ { 2 } + | x | + 6$
A) Odd
B) Neither
C) Even

Question

Quizplus · Accepted Answer

The function $f(x) = 0.25x^2 + |x| + 6$ is even because it remains unchanged when $x$ is replaced with $-x$. The term $0.25x^2$ is even since $(0.25)(-x)^2 = 0.25x^2$, and $|-x| = |x|$. The constant term $6$ is symmetric about the y-axis. All these components satisfy the definition of an even function, where $f(x) = f(-x)$.

Determine If the Function Is Even, Odd, or Neither f(x)=0.25x2+∣x∣+6f ( x ) = 0.25 x ^ { 2 } + | x | + 6f(x)=0.25x2+∣x∣+6

Determine If the Function Is Even, Odd, or Neither $f ( x ) = 0.25 x ^ { 2 } + | x | + 6$