Question

Can an absolute value function also be a polynomial function? Why or why not?​

Answer 1

For this case a polynomial is defined with the following expression:

`p(x) =\sum_(i=1)^n a_i x^i`For all x on the domain considered and n is finite

And by definition the absolute value function is defined as:

`|x|= x, x \geq 0`

`|x| =-x , x<0`

If we use the function
`f(x) =|x|` we see that is impossible to obtain the general expression of a polynomial since we can't obtain the form |x| and since we don't satisfy the definition the answer would be:

An absolute value function CANNOT be considered as a polynomial function

Explanation:

For this case a polynomial is defined with the following expression:

`p(x) =\sum_(i=1)^n a_i x^i`For all x on the domain considered and n is finite

And by definition the absolute value function is defined as:

`|x|= x, x \geq 0`

`|x| =-x , x<0`

If we use the function
`f(x) =|x|` we see that is impossible to obtain the general expression of a polynomial since we can't obtain the form |x| and since we don't satisfy the definition the answer would be:

An absolute value function CANNOT be considered as a polynomial function