Algebra Functions Domain and range Domain of a function Domain and Range of a Relation Domain and Range of a Function Given a Formula Domain and Range 1 Domain of a Radical Function Domain of a function Domain and Range 2 Domain and Range of a Function Range of a function Domain and range Domain and Range 1 Domain and Range 1 Practice this concept Back Domain and Range 1 ⇐ Use this menu to view and help create subtitles for this video in many different languages. You'll probably want to hide YouTube's captions if using these subtitles. 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. Questions Tips & Feedback Be specific, and indicate a time in the video: At 5:31, how is the moon large enough to block the sun? Isn't the sun way larger? Have something that's not a question about this content? Post a tip or feedback General discussion about the site Report a technical problem with the site Request a video or feature This discussion area is not meant for answering homework questions. Formatting tips Cancel or ( total) Share a tip When naming a variable, it is okay to use most letters, but some are reserved, like 'e', which represents the value 2.7831... Suggest a fix At 2:33, Sal says "double bonds" but should say "single bonds." Have something that's not a tip or feedback about this content? Ask a question General discussion about the site Report a technical problem with the site Request a video or feature This discussion area is not meant for answering homework questions. Formatting tips Cancel or Discuss the site For general discussions about Khan Academy, visit our Reddit discussion page. Flag inappropriate posts Here are posts to avoid making. If you do encounter them, flag them for attention from our Guardians. abuse disrespectful or offensive an advertisement not helpful low quality not about the video topic soliciting votes or seeking badges a homework question a duplicate answer repeatedly making the same post wrong category a tip or feedback in Questions a question in Tips & Feedback an answer that should be its own question about the site a question about Khan Academy (Visit our FAQ) a post about badges a technical problem with the site (Report a problem) a request for videos or features
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