Determine whether the power function is even, odd, or neither.
-$$f ( x ) = - 7 x ^ { 4 / 7 }$$
A) Even
B) Odd
C) Neither

Question

Quizplus · Accepted Answer

A power function $f(x) = ax^n$ is even if $n$ is an even number, odd if $n$ is an odd number, and neither if $n$ does not satisfy these conditions. However, the distinction between even and odd functions also depends on their symmetry: even functions are symmetric about the y-axis, and odd functions are symmetric about the origin. In this case, $f(x) = -7x^{4/7}$, the exponent $4/7$ is not an integer, making the direct even/odd integer rule inapplicable. However, since $f(-x) = -7(-x)^{4/7} = -7x^{4/7} = f(x)$, the function is even because it satisfies the condition $f(-x) = f(x)$, indicating symmetry about the y-axis.

Determine Whether the Power Function Is Even, Odd, or Neither f(x)=−7x4/7f ( x ) = - 7 x ^ { 4 / 7 }f(x)=−7x4/7

Determine Whether the Power Function Is Even, Odd, or Neither $f ( x ) = - 7 x ^ { 4 / 7 }$