Question

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

Answer 1

Answer:

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

Step-by-step 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