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Eric is selling raffle tickets for a school fundraiser.

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Each ticket costs $3, and he knows the amount of money he

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collects is a function of how many tickets he sells.

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What are the domain and range for that function?

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So let's write the function for how

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much money he collects.

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So I'll call that m, the function will be m, and it's a

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function of how many tickets he sells.

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So it's a function of t, for tickets.

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So m, the amount of money collected, is a function of

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the number of tickets he sells.

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That's a pretty straightforward function.

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Every ticket costs $3.

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He gets $3 for every ticket.

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So it's going to be 3 times t dollars or 3t dollars.

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That's how much money he collects.

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Now they ask us, what are the domain and

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range for that function?

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It sounds all fancy and difficult, but just remember

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the domain, this just means, what can I

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input into the function?

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So another way to think about is what are the possible t's

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that can be input into this function?

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The range is, what are the possible values that the

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function can take on?

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So think about it.

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You might at first say I could put any t there, but think

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about the actual reality of what he's doing.

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He's selling tickets, and so he can't

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sell negative tickets.

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He might sell 0 tickets, and he might

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sell a gazillion tickets.

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I guess he could sell an infinite amount of tickets.

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At some point that becomes unrealistic.

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But he definitely can't sell negative tickets.

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He also is not going to sell half of a ticket.

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Every ticket he sells is a whole number, it's an integer.

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So the domain for this function, we could say t has

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to be a non-negative integer.

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I think that covers what I just talked about.

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Non-negative.

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Instead of saying positive, because it could be 0.

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He might literally sell no tickets.

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He can't sell a negative 1 ticket or negative 2, so it's

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anything that's non-negative.

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It has to be an integer, he can't sell half of a ticket,

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so, and he definitely-- it has to be an integer.

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So that's our domain,.

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And let's think about what our range is.

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A range is the possible values that we can take on.

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If t is always going to be a non-negative integer, then

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what's 3t always going to be?

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Well it's going to be a non-negative multiple of 3.

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So non-negative multiples of 3.

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Think about it.

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He'll never be able to collect $2, because he could either

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sell 0 tickets and get nothing.

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Let me write this down.

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He might sell 0 tickets, so m of 0, he's going to get $0.

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m of, if he sells one ticket, he's going to get $3.

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If he sells two tickets, he's going to get $6.

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So he's never going to be able to get 2 or 4.

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Every possible value for the amount of money he collects

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for our function has to be a multiple of 3.

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

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because the domain is non-negative integers.

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