Question

Jackson has a gift card for $120 to use at a department store. he wants to purchase 2 shirts and 3 pairs of pants with his gift card. if x represents the cost of the shirts and y represents the cost of the pants, what are the domain and range of this relationship?

Answer 1

• The domain of this relationship can be defined as,

0 ≤ x ≤ 60

• The range of this relationship can be defined as,

0 ≤ y ≤ 40

Definition of Domain and Range

The set of  all the possible input values for which the provided function is defined is termed as the domain of that function.

The set of all the possible values that a given function can generate as an output is termed as the range of that function.

Forming the Relation

It is given that,

• Jackson wants to purchase 2 shirts and 3 pairs of pants with his gift card

• x represents the cost of the shirts and y represents the cost of the pants

• The limit of the gift card = $120

Thus, the relation formed is given by,

$2x + 3y \leq 120$

Domain and Range of the Given Relation

We have,

$2x + 3y \leq 120$

⇒ $2x \leq 120$

⇒ $x\leq60$

Thus, the domain is given by,

⇒ $0\leq x\leq 60$

Similarly,

$3y\leq 120$

⇒ $y\leq 40$

Thus, the range is given by,

⇒ $0\leq y\leq 40$

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