In the given function, y represents the amount of money left on a public transit pass, and x represents the number of rides on the subway. To determine the domain and range, let's analyze each:
Domain: The domain of a function is the set of all possible input values (independent variable). In this case, x represents the number of rides on the subway. It should be a non-negative whole number since you can't have a negative or fractional number of subway rides. Therefore, the domain is all non-negative integers, or in interval notation:
Domain (x): [0, ∞)
Range: The range of a function is the set of all possible output values (dependent variable). In this case, y represents the amount of money left on the transit pass. The range depends on the initial amount of money on the pass and how much each subway ride costs. Since the function is y = 17 - 2.75x, it implies that for each subway ride (x), 2.75 dollars are subtracted from the initial balance of 17 dollars. The range depends on the minimum balance possible.
To find the minimum balance (minimum y), set the function equal to zero and solve for x:
17 - 2.75x = 0
2.75x = 17
x = 17 / 2.75 ≈ 6.18
This means that after approximately 6 subway rides (rounded up to the nearest ride), the balance will reach zero, and no further rides can be taken without adding more money. So, the range consists of all non-negative real numbers less than or equal to 17, including zero. In interval notation:
Range (y): [0, 17]
To summarize:
Domain (x): [0, ∞)
Range (y): [0, 17]