Eric is selling raffle tickets

for a school fundraiser. Each ticket costs $3, and he

knows the amount of money he collects is a function of how

many tickets he sells. What are the domain and range

for that function? So let’s write the

function for how much money he collects. So I’ll call that m, the

function will be m, and it’s a function of how many

tickets he sells. So it’s a function of

t, for tickets. So m, the amount of money

collected, is a function of the number of tickets

he sells. That’s a pretty straightforward

function. Every ticket costs $3. He gets $3 for every ticket. So it’s going to be 3 times

t dollars or 3t dollars. That’s how much money

he collects. Now they ask us, what

are the domain and range for that function? It sounds all fancy and

difficult, but just remember the domain, this just

means, what can I input into the function? So another way to think about

is what are the possible t’s that can be input into

this function? The range is, what are the

possible values that the function can take on? So think about it. You might at first say I could

put any t there, but think about the actual reality

of what he’s doing. He’s selling tickets,

and so he can’t sell negative tickets. He might sell 0 tickets,

and he might sell a gazillion tickets. I guess he could sell an

infinite amount of tickets. At some point that becomes

unrealistic. But he definitely can’t

sell negative tickets. He also is not going to

sell half of a ticket. Every ticket he sells is a whole

number, it’s an integer. So the domain for this function,

we could say t has to be a non-negative integer. I think that covers what

I just talked about. Non-negative. Instead of saying positive,

because it could be 0. He might literally

sell no tickets. He can’t sell a negative 1

ticket or negative 2, so it’s anything that’s non-negative. It has to be an integer, he

can’t sell half of a ticket, so, and he definitely– it

has to be an integer. So that’s our domain,. And let’s think about

what our range is. A range is the possible values

that we can take on. If t is always going to be a

non-negative integer, then what’s 3t always going to be? Well it’s going to be a

non-negative multiple of 3. So non-negative multiples

of 3. Think about it. He’ll never be able to collect

$2, because he could either sell 0 tickets and

get nothing. Let me write this down. He might sell 0 tickets, so m

of 0, he’s going to get $0. m of, if he sells one ticket,

he’s going to get $3. If he sells two tickets,

he’s going to get $6. So he’s never going to be

able to get 2 or 4. Every possible value for the

amount of money he collects for our function has to

be a multiple of 3. It’s going to be a non-negative

multiple of 3 because the domain is

non-negative integers.

## 11 Comments

## paulceltics

great thanks

## itsmeTIBOR

You better be getting paid $80k+ / year, you are better than my math teacher! 🙂

## Y V

very intuitive.. thanks so much!

## Devon Lewis

He's getting paid ALOT more through youtube 🙂

## CombustibleLemon72

Oh, wow these math questions are so applicable to everyday life.

But seriously, your videos are awesome. *gives cookie*

## Nikola Nedeljkovic

Like if ur math teacher sucks

## Carson Vandegriffe

We do independant learning at our school and some of concepts are not explained well is Saxon, Thx

## Thomas Rad

Instead of the domain being the set off all negative intergers, you could just say that the domain could be all whole numbers (0,1,2,3,4…..)

## Thomas Rad

All non-negative **

## Dolbo Dolb

domain and range are the two most stupid ambiguously sounding pairs of terms. either one can be thought of as X. or Y. totally arbitrary names. how about we call them red and black.

## TheProgrammingJedi

awesome