Question

Which of the following is not an equation of a simple, even polynomial function? y = | x | y = x2 y = x3 y = -x2

Answer 1

The equation
`y=x^3` is not an equation of a simple , even polynomial function.

Explanation:

Even function : A function is even when its graph is symmetric with respect to y-axis.

Algebrically , the function f is even if and only if

f(-x)=f(x) for all x in the domain of f.

When the function does not satisfied the above condition then the function is called non even function.

f(x)
`\\eq` f(-x)

Now , we check given function is even or not

A. y=
`\mid x\mid`

If x is replaced by -x

Then we get the function

f(-x)=
`\mid -x \mid`

f(-x)=
`\mid x \mid`

Hence, f(-x)=f(x)

Therefore , it is even polynomial function.

B.
`y=x^2`

If x is replace by -x

Then we get

f(-x)=
`(-x)^2`

f(-x)=
`x^2`

Hence, f(-x)=f(x)

Therefore, it is even polynomial function.

C.
`y=x^3`

If x is replace by -x

Then we get

f(-x)=
`(-x)^3`

f(-x)=
`-x^3`

Hence, f(-x)
`\\eq` f(x)

Therefore, it is not even polynomial function.

D.
`y= -x^2`

If x is replace by -x

Then we get

f(-x)= -
`(-x)^2`

f(-x)=-
`x^2`

Hence, f(-x)=f(x)

Therefore, it is even polynomial function.

Answer: C.
`y=x^3` is not simple , even polynomial function.

Answer 2

• y = | x |
• y = x^3

Explanation:

The absolute value function prevents the expression from being a polynomial. The degree of 3 in y^3 is an odd number so that polynomial function will not be even.