To determine whether the number of customers who have come into Trent's Hobby Shop each day forms a discrete or continuous function, let's first understand these two concepts:
1. Discrete Functions:
- These functions take on distinct, separate values.
- They typically involve countable scenarios, meaning the function only takes on specific values, usually integers.
- Examples: Number of students in a class, number of cars in a parking lot, etc.
2. Continuous Functions:
- These functions take on an unbroken range of values.
- They involve scenarios where the variables can take any value within a given range, including fractions and decimals.
- Examples: Temperature, distance, weight, etc.
Considering the function in question, which shows the number of customers on different days:
- The number of days is a discrete variable because each day is an individual, countable unit.
- The number of customers is also a discrete variable because you can only count whole customers (you can't have a fraction of a customer).
Therefore, since the number of customers can only be counted in whole numbers and does not take on any fractional values, the function representing the number of customers per day is a discrete function.
Thus, the function is discrete.
