Is the function $f (x) = 2 x^{4} + 3 x^{2}$ $f(x)=2x^4+3x^2$ even, odd or neither?

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Is the function $f (x) = 2 x^{4} + 3 x^{2}$ $f(x)=2x^4+3x^2$ even, odd or neither?

1 Answer

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Answer 1 · 2015-07-15T02:01:35

EVEN

Explanation:

If it is:
EVEN then: $f (- x) = f (x)$ $f(-x)=f(x)$
ODD then: $f (- x) = - f (x)$ $f(-x)=-f(x)$

Let us try with:
$x = 2$ $x=2$
$f (2) = 2 \cdot 2^{4} + 3 \cdot 2^{2} = 59$ $f(2)=2*2^4+3*2^2=59$
and:
$x = - 2$ $x=-2$
$f (- 2) = 2 \cdot {(- 2)}^{4} + 3 \cdot {(- 2)}^{2} = 59$ $f(-2)=2*(-2)^4+3*(-2)^2=59$
so:
$f (- 2) = f (2)$ $f(-2)=f(2)$ or $f (- x) = f (x)$ $f(-x)=f(x)$

Graphically:
graph{2x^4+3x^2 [-16.02, 16.02, -8.01, 8.01]}
(basically the left side is a reflection about the $y$ $y$ axis of the right side)

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Is the function $f (x) = 2 x^{4} + 3 x^{2}$ $f(x)=2x^4+3x^2$ even, odd or neither?

1 Answer

Explanation:

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