Question

What are the domain and range of the absolute value parent function?

Answer 1

Answer:

The domain is all real numbers and the range is non-negative real numbers

(y ≥ 0) ⇒ answer B

Step-by-step explanation:

* Lets revise the parent function of the absolute value

- The absolute value or modulus |x| of a real number x is the

  non-negative value of x

- The absolute value of a number means the magnitude of the number

  without regard to its sign

- The parent function of the absolute value is f(x) = IxI

∵ The domain of the function is all the values of x which make the

  function defined

∵ In the function f(x) = IxI, x can be any number

∴ The domain of the f(x) is any real number

∴ The domain is (-∞ , ∞) or {x : x ∈ R}

∵ The range is the set of values of y that corresponding with the

   domain

∵ f(x) = IxI is non-negative value

∴ f(x) ≥ 0

∵ f(x) = y

∴ y ≥ 0

∴ The range is the set of real numbers greater than or equal zero

∴ The range is [0 , ∞) or {y : y ≥ 0}

* The true statement is: The domain is all real numbers and the range is

  non-negative real numbers (y ≥ 0)