Question

Domain and range pls help!!

A group of friends is planning a trip to a local amusement park. They are taking a bus which holds 32 people. It will cost $25 for parking and tickets to the park are $22.50 per person. The equation that models this situation is:
c(x) = 22.5x + 25, where c represents the cost for the group to go to the park and x represents the number of people who go on the trip.

1. Is this function discrete or continuous and why?
2. What is an appropriate domain for this problem?
3. What is an appropriate range for this problem?
4. What does the ordered pair (20, 140) mean in the context of this problem?

Answer 1

1. This function is continuous because it represents a real-world situation where the number of people can take on any value between whole numbers.
2. The appropriate domain for this problem would be the set of whole numbers greater than or equal to 0, since you can't have a negative number of people going on the trip and the number of people must be a whole number.
3. The appropriate range for this problem would be the set of real numbers greater than or equal to the cost of parking ($25) since the cost of the tickets can vary depending on the number of people going on the trip.
4. The ordered pair (20, 140) means that if 20 people go on the trip, the total cost for the group would be $140.

Answer 2

Certainly, here are the answers to each question:

The function is continuous.

The appropriate domain for this problem is x ≥ 0.

The appropriate range for this problem is c ∈ ℝ (all real numbers).

The ordered pair (20, 140) means that with 20 people going on the trip, the cost for the group will be $140.

Explanation:

This function is continuous. A continuous function can take on any real number value within its domain. In this case, the number of people (x) can be any non-negative real number (including fractions), and the cost (c) can also be any real number (including fractions) depending on the number of people. There are no "gaps" or jumps in the function, making it continuous.

The appropriate domain for this problem is a non-negative real number. In the context of this problem, it doesn't make sense to have a negative number of people, and you can have any non-negative number of people joining the trip. So, the domain is x ≥ 0.

The appropriate range for this problem is the set of real numbers representing the cost of the trip. Since the cost can vary depending on the number of people (including fractions of a person), the range includes all real numbers. So, the range is c ∈ ℝ (where ℝ represents the set of real numbers).

The ordered pair (20, 140) means that if 20 people go on the trip, the cost for the group will be $140. In other words, when x (the number of people) is 20, the function c(x) returns a value of 140, indicating that it will cost $140 for the group of 20 people to go on the trip, considering the ticket price and parking fee