Question

Which statement about y = x2 − x3 is true?

Answer 1

ANSWER

c.It is neither an odd nor an even function.

EXPLANATION

The given function is

$y = f(x) = {x}^{2} - {x}^{3}$

If this function is odd, then f(-a)=-f(a).

$f( - a) = {( - a)}^{2} - {( - a)}^{3}$

$f( - a) = {( a)}^{2} + {( a)}^{3}$

Now ,

$f( a) = {( a)}^{2} - {( a)}^{3}$

$- f( a) = - {( a)}^{2} + {( a)}^{3}$

Since

$f( - a) \ne - f(a)$

The function is not odd.

Also if the function is even, then

$f( a) = f( - a)$

Since

$f( a) \ne f( - a)$

the function is not even.

Hence the function is neither even nor odd.

Answer 2

Answer:

Option c. It is neither an odd nor an even function.

Step-by-step explanation:

The equation $y = x^2 - x^3$ is a function, because there is a single value of y for each value of the domain x.

To test if it is an even function we must do  $y = f(-x)$. If $f(-x) = f(x)$ then it is an even function.

If $f(-x) = -f(x)$ then it is an odd function

$y = f(-x) = (-x) ^ 2 - (- x) ^ 3$

Simplifying we have:

$y = x ^ 2 + x ^ 3$

f(-x) is not equal to f(x) so the function is not even.

f(-x) is not equal to -f(x) so the function is not odd.

THE correct answer is the option c