Interpreting function notation
Let P of t denote the number of people P at the Copacabana beach in Rio de Janeiro, t hours past midnight on a specific day. What does the statement P of 5 less than P of 9 mean? So before I read these, let's think about this. So this is the number of people five hours past midnight on a specific day. So this is saying that the number of people five hours past midnight is less than the number of people nine hours past midnight at Copacabana beach. So the number of people five hours past midnight is less than the number people nine hours past midnight. Let's get into these choices. The time at which there were five people at the beach is earlier than the time there were nine people. Who know? -- the five and the nine aren't the number of people This is the time. This is the input into the function. The input into the function is time. This gives people as a function of time. You give a time. You give a time. This function P, it outputs P of t, which is equal to the number of people number of people on the beach at time, at time t. So this five -- this is the input. This is the time five hours after I shouldn't say time t. I guess you could say a.m. time -- t hours past midnight at t hours past midnight, hours past past midnight. midnight. So we can definitely rule this out. This isn't talking about five people or nine people. This is talking about five hours after midnight is input and how many people we have five hours after midnight is how many people we have nine hours after midnight. 5 a.m. is an earlier time the 9 a.m. Well, that is a true statement but that's not what this statement is saying. It's not -- this isn't giving us information which is no from, I guess, how we think about time or how we measure time. the 5 a.m. is earlier than 9 a.m. but that's not what this statement is trying to say. So rule that out. There were more people at the beach at 9 a.m. So to be clear, people at the beach at 9 a.m. that's that right over here -- than there were -- than there were at 5 a.m. -- than there were at 5 a.m. Well, that's right over there. And we see -- we see this quantity here is greater than those magenta quantity is indeed greater than this green quantity. The green quantity is less than the magenta quantity, so we would definitely pick that one.