Faith Welch

2022-07-25

Evaluate. $f\left(x\right)={x}^{3}﻿-4x$

nezivande0u

A function is said to be even if and only if
f(x)=f(-x)
a function is said to be odd if and only if
-f(x)=f(-x)
sp we got:
$f\left(x\right)={x}^{3}-4x$
lets work on f(-x) because is unavoidable
if a function is even, it can't be odd
$f\left(-x\right)=\left(-x{\right)}^{3}-4\left(-x\right)=-{x}^{3}+4x$
now lets work on the even function
f(x)=f(-x)
${x}^{3}-4x=-{x}^{3}+4$ false, so this os not even function
checking for odd-function:
$-f\left(x\right)=-\left({x}^{3}-4x\right)=-{x}^{3}+4x$
$-{x}^{3}+4x=-{x}^{3}+4x$

Greyson Landry

For this equation,
Evenmeans, that the graphed line is symmetric to the y-axis. Odd meansthat the graphed line is symmetric to the y-axis. To figure if afunction is even or odd, you change the variables. For thisequation, the line is, an odd function. This is because, if youchange the x's to -x's (even function) it is not the same equation.If, you change the x's to -x's and the y's to -y's (odd function)it is the same equation. Example: (even)
$f\left(x\right)={x}^{3}-4x\ne f\left(x\right)=-\left({x}^{3}\right)-\left(-4x\right)$ (odd)
$f\left(x\right)={x}^{3}-4x=f\left(-x\right)=-\left({x}^{3}\right)-\left(-4x\right)$

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