Question

Which of the following is the parent function of all absolute value functions? f(x) = 3x f(x) = |x| f(x) = 2|x|

Answer 1

The parent function of all absolute value functions is:

f (x) = absolute value of x

to illustrate the validity of the claim, substitute any whole number or a combination of a whole number and a variable to "x". For example,

let x = 4x; so, f(x) = absolute value of (4x)

the parent function of this new function is still f(x) = abs (x)

Answer 2

f(x) = |x|

Explanation:

Absolute function is always represented by symbol | |

f(x) = 3x , f(x) is a linear function because we have 3x. there is no absolute sign. So it is not an absolute value function.

`f(x) = |x|` It has absolute value symbol. Also there is no other number multiplied or added inside or outside the absolute value symbol. So it is a parent function of all absolute value functions.

f(x) = 2|x| . It has absolute value symbol. But 2 is multiplied with |x| that make changes in the function f(x). So it cannot be a parent function.