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

Answer:

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

Step-by-step 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)$\neq$ 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)$\neq$ 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

Answer:

• y = | x |
• y = x^3

Step-by-step 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.