Calculus-Even and odd functions?

Question

Is this function odd/even or neither? Give reasons for your answer...

f(x)= | x^3 |

Thats absolute value of x to the exponent 3

Answer 1

Even function means f(-x) = f(x)

Odd function means f(-x) = -f(x)

So, you just need to plug in values and see what happens.

If x = 2

f(2) = 8
f(-2) = 8

This shows an even function.

If x = -5
f(-5) = 125
f(5) = 125

Also shows an even function.

Answer 2

Rember that an even function is a funciton such that f(-x) = f(x).

f(-x) = | (-x)^3 | = | (-1)^3 x^3 | = | -1 * x^3 | = | x ^3 | = f(x)

So by definition, this is an even function.

Answer 3

f(-x) = | (-x)^3 | = | -x^3 | = | x^3 | = f(x)
Therefore, f(x) is an even function.