olivernolasco23
contestada

Which statement about y = x2 − x3 is true?
a.It is not a function.

b.It is an even function.

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

d.It is an odd function.

Respuesta :

kudzordzifrancis

ANSWER

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

EXPLANATION

The given function is

[tex]y = f(x) = {x}^{2} - {x}^{3} [/tex]

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

[tex]f( - a) = {( - a)}^{2} - {( - a)}^{3} [/tex]

[tex]f( - a) = {( a)}^{2} + {( a)}^{3} [/tex]

Now ,

[tex]f( a) = {( a)}^{2} - {( a)}^{3} [/tex]

[tex] - f( a) = - {( a)}^{2} + {( a)}^{3}[/tex]

Since

[tex]f( - a) \ne - f(a)[/tex]

The function is not odd.

Also if the function is even, then

[tex]f( a) = f( - a)[/tex]

Since

[tex]f( a) \ne f( - a)[/tex]

the function is not even.

Hence the function is neither even nor odd.

luisejr77

Answer:

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

Step-by-step explanation:

The equation [tex]y = x^2 - x^3[/tex] 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  [tex]y = f(-x)[/tex]. If [tex]f(-x) = f(x)[/tex] then it is an even function.

If [tex]f(-x) = -f(x)[/tex] then it is an odd function

[tex]y = f(-x) = (-x) ^ 2 - (- x) ^ 3[/tex]

Simplifying we have:

[tex]y = x ^ 2 + x ^ 3[/tex]

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

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