Question

function p represents the number of people in the library on a monday as a function of hours since the library opened. here is the graph of function p. based on the graph and the situation, which domain and range make sense for function p? select the correct choice.

Explanation:

Since the problem is about determining the domain and range of a function representing the number of people in a library over time, and no specific options are provided here, I'll assume a typical scenario.

• Domain: The domain represents the hours since the library opened. From the graph, the time starts at 0 (opening) and goes up to 14 hours (when the number of visitors reaches 0 again). So the domain is all real numbers from 0 to 14, or \( 0 \leq t \leq 14 \) where \( t \) is time in hours.
• Range: The range represents the number of visitors. From the graph, the number of visitors starts at 0 (when the library opens) and goes up to a maximum of 80 (or slightly more, but typically around 0 to 80+). So the range is all real numbers from 0 to the maximum number of visitors, say \( 0 \leq p(t) \leq 80 \) (or a bit higher based on the peak, but the key is non - negative values up to the peak).

If we assume common options (for example, if options were like:
A. Domain: \( 0\leq t\leq14 \), Range: \( 0\leq p(t)\leq80 \)
B. Domain: \( 0\leq t\leq10 \), Range: \( 0\leq p(t)\leq60 \)
C. Domain: \( 0\leq t\leq12 \), Range: \( 0\leq p(t)\leq70 \)
D. Domain: \( 0\leq t\leq15 \), Range: \( 0\leq p(t)\leq90 \))

The correct option would be A as the graph shows time from 0 to 14 hours and the number of visitors from 0 to around 80 (the peak).

Answer:

A. Domain: \( 0\leq t\leq14 \), Range: \( 0\leq p(t)\leq80 \)