Which of the following graphs is neither even nor odd?
A)$f ( x ) = \frac { 4 x ^ { 2 } } { x ^ { 4 } + 1 }$
B) $f ( x ) = 8 x ^ { 3 } + 10 x ^ { 2 } + 1$
C) $f ( x ) = x ^ { 3 } - 9 x$

Question

Which of the following graphs is neither even nor odd? 
A)$f ( x ) = \frac { 4 x ^ { 2 } } { x ^ { 4 } + 1 }$
B) $f ( x ) = 8 x ^ { 3 } + 10 x ^ { 2 } + 1$
C) $f ( x ) = x ^ { 3 } - 9 x$

Quizplus · Accepted Answer

A function is even if $f(x)=f(-x)$ for all $x$ in its domain, and odd if $f(-x)=-f(x)$ for all $x$ in its domain. For function A, we can verify that it is even using algebra: $$f(x)=f(-x)\implies \frac{4x^2}{x^4+1}=\frac{4(-x)^2}{(-x)^4+1}\implies \frac{4x^2}{x^4+1}=\frac{4x^2}{x^4+1}$$ Therefore, function A is even. For function C, we can verify that it is odd using algebra: $$f(-x)=-f(x)\implies (-x)^3-9(-x)=-(x^3-9x)\implies -x^3+9x=x^3-9x$$ Therefore, function C is odd. However, for function B: $$f(-x)
eq -f(x)$$ We can verify this using algebra too: $$f(-x)=8(-x)^3+10(-x)^2+1=-8x^3+10x^2+1
eq -8x^3-10x^2+1=-f(x)$$ Therefore, function B is neither even nor odd.

Which of the Following Graphs Is Neither Even nor Odd f(x)=4x2x4+1f ( x ) = \frac { 4 x ^ { 2 } } { x ^ { 4 } + 1 }f(x)=x4+14x2​

Which of the Following Graphs Is Neither Even nor Odd $f ( x ) = \frac { 4 x ^ { 2 } } { x ^ { 4 } + 1 }$