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### Course: Algebra (all content) > Unit 7

Lesson 4: Interpreting function notation# Function notation word problem: beach

Learn how to interpret expressions that contain a function within a real-world context. In this video, the function we interpret models the number of people at the beach over time.

## Want to join the conversation?

- Wouldn't it be obvious that there would be more ppl at 5 am than 9 am? It seemed obvious to me.(0 votes)
- That's not the point of the question. It is just an example to allow us to develop a stronger understanding of functions before we tackle harder real-life situations that don't seem as "obvious".(27 votes)

- Hey guys! This might not be the right place to ask this question but I am having trouble figuring out what to do with a question given to me by my math teacher. The equation is g(x) = 3x^2 + x and it says find x, if g(x) =2, how would I solve this any suggestions?(2 votes)
- 3x^2 + x = 2. then just solve for x. But I don't think this will help as your assignment would be 2 years late.(9 votes)

- hello can someone help me out with this question :

What does this mean?

g(x) has y-values greater than f(x) for x-values between -2 and 2. What will the mathematical notation be for this?

I don't understand(4 votes)- My guess is this :- g(x) > f(x), when x = {-1,0,1}(2 votes)

- In 1980 high school dropouts were 5212 thousand. by 2008 the number dropped to 3118 thousand. what's the linear function that models the decrease?(2 votes)
- I'm not sure but I'll try. The number of dropouts (say d) is dependent on the year (say y). So d will be a function of y, f(y)=d and since the number d appears to decrease by 74,785 per year since 1980, d for the current year would be less by f(y)=74,785 (y-1980)(5 votes)

- when he says that5:00am is earlier than9:00am, he is wrong, isn't he? Because9:00is a whole 20 hours before5:00am. Someone explain.(2 votes)
- A day technically starts right after midnight.5:00am is earlier in the morning than9:00am.

When you add 20 hours, you are now in the next day.

Hope this helps.(4 votes)

- At choice C, we wouldn't know if there were more people at the beach at 9am than there were at 5am! So wouldn't choice C be incorrect?(2 votes)
- You aren't asked to verify the accuracy of the statement. You are asked to interpret what it means. Item C is the correct interpretation for what the statement is saying.(4 votes)

- Kaori is taking a free-throw.

H(d) models the basketball's height (in meters) at a horizontal distance of d meters from Kaori.

What does the statement H(R) = 4 mean?

(Choice A) At a horizontal distance of 4 meters from Kaori, the ball's height was equal to R meters.

(Choice B) The ball was at the same height at the horizontal distances of 4 meters and R meters.

(Choice C) At a horizontal distance of R meters from Kaori, the ball's height was equal to 4 meters.

Where does the variable R come from?(2 votes)- It looks like "R" represents the input to the function and 4 is the output. You need to pick the correct choice which matches that situation.(3 votes)

- At2:07, how would choice B be incorrect if 5am is an earlier time than 9am?(2 votes)
- You need to interpret the statement: p(5)<p(9)

This is not comparing time. This compares the output of the functions, which is numbers of people at the beach at 5am vs at 9am. So, you need to pick an answer that is related to people.

The expression is saying there are fewer people on the beach at 5am than at 9am. This is item C, but in reverse.(3 votes)

- this is a bit irrelevant, but at 0.05, the line about the number of people P at the Copacabana beach has always bugged me when i realised it(p ≈ urine)

does anyone know how to unsee something?(2 votes) - i can't Understand How a limit's value at a limit is undefinite(2 votes)

## Video transcript

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.