Domain

When you order food through a delivery app, the delivery fee often depends on your distance from the restaurant. We can represent this using a function. The delivery distance is the input, and the delivery fee is the output.

To identify which values the function can accept, we need to find its domain. The domain is the set of all input values for which the function is defined.

In real-life situations, practical limits help define the domain. For example, a delivery distance cannot be negative.

Suppose the app delivers to customers who live more than 0 kilometers away but no farther than 10 kilometers from the restaurant. If x represents the delivery distance, the domain includes values of x greater than 0 and less than or equal to 10.

A function’s algebraic rule can also limit its domain. For example, consider a function with x minus 5 in the denominator. If we substitute x equals 5, the denominator becomes 0, and division by zero is undefined. So, the domain includes all real numbers except 5.

Finding the domain helps us identify valid input values, interpret the function correctly, and understand the model's limits.