The function y =∣ x + 2 ∣ − 2 is defined at every real number so its domain is -∞ < x < ∞.
A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.
The domain is for the independent variable while the range is for the dependent variable.
For example f(x) = x²
Now if we put x = 1 then it is called as domain variable while the value of functin at x = 1 its that f(1) = 1 called range variable.
Given the function y =∣ x + 2 ∣ − 2
At x = -2 ⇒ y = ∣ -2 + 2 ∣ - 2 = -2
For every x > -2 , ∣ x + 2 ∣ is positive and for every x < -2 , ∣ x + 2 ∣ will also positive since it is mode function.
So all values of a real number will result in a definite value of the function.
Hence "The function y =∣ x + 2 ∣ − 2 is defined at every real number so its domain is -∞ < x < ∞".
For more details about the range and domain of the function,
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