Question

hours since opening
select one: based on the graph and the situation, which domain and range make sense for function p?
a. domain: all numbers from 0 to 85. range: all numbers from 0 to 14.
b. domain: whole numbers only from 0 to 14. range: whole numbers only from 0 to 85.
c. domain: all numbers from 0 to 14. range: whole numbers from 0 to 85.
d. domain: whole numbers only from 0 to 14. range: all numbers from 0 to 85.

Explanation:

To determine the correct domain and range for the function related to "hours since opening", we analyze the context:

• Domain (input, hours since opening): Hours since opening should be non - negative whole numbers (you can't have negative hours of operation) and likely has a maximum (e.g., a business is open for a certain number of hours, say up to 14 hours a day). So the domain is whole numbers from 0 to 14.
• Range (output, likely related to some quantity like customers or sales): The range values (the output of the function) are whole numbers (you can't have a fraction of a customer or a non - whole number of sales in many cases) and likely go up to 85 (as per the options).

Now let's analyze each option:

• Option A: Domain is all numbers from 0 to 85 (incorrect, hours since opening shouldn't go up to 85, it's about hours of operation, not the output quantity) and range is all numbers from 0 to 14 (incorrect, range should be related to the output, not the input hours).
• Option B: Domain is whole numbers only from 0 to 14 (good for hours of operation) but range is whole numbers only from 0 to 85 (the word "only" is incorrect as the range could potentially be all whole numbers up to 85, not just "only" in a restrictive sense that doesn't match the context of a function's range for a real - world situation like business operations).
• Option C: Domain: all numbers from 0 to 14 (hours since opening, non - negative, up to 14 hours is reasonable) and Range: whole numbers from 0 to 85 (the output, like number of customers or sales, is a whole number and up to 85 is reasonable). This matches the context of a function for a business - related situation (e.g., hours open and number of customers/sales).
• Option D: Domain is whole numbers only from 0 to 14 (the "only" is incorrect as the domain is about hours of operation, which are whole numbers from 0 to 14, but the description "only" is not the right way to put it) and range is all numbers from 0 to 85 (range should be whole numbers as you can't have a fraction of a customer/sale).

Answer:

C. Domain: all numbers from 0 to 14. Range: whole numbers from 0 to 85.