FIND DOMAIN AND RANGE OF ABSOLUTE VALUE FUNCTION

Domain :

The set of all possible inputs is known as domain. For absolute value functions all real numbers will be domain.

Because there is no restriction to give inputs. So, for all absolute value functions domain will be  (-∞, ∞).

Range :

This graph will not go below -2 on y-axis. So, range is

-2 ≤ y ≤∞

Find the domain and range of each function

Problem 1 :

y = │x│

Solution : 

Domain : (-∞, ∞), x ∈ R

Range : [0, ∞), y ≥ 0

Problem 2 :

y = -│x│

Solution :

Domain : (-∞, ∞), x ∈ R

Range : [0, -∞), y ≤ 0

Problem 3 :

y = │x + 2│+ 3

Solution :

Domain: (-∞, ∞), x ∈ R

Range: [3, ∞), y ≥ 3

Problem 4 :

y = │x│- 5

Solution :

Domain: (-∞, ∞), x ∈ R

Range: [-5, ∞), y ≥ -5

Problem 5 :

y = -│x│- 9

Solution :

Domain: (-∞, ∞), x ∈ R

Range: [-9, -∞),  y ≤ -9

Problem 6 :

y = -│x - 3│+ 10

Solution :

Domain: (-∞, ∞), x ∈ R

Range: [10, -∞), y ≤ 10