Domain of modeling functions | Functions and their graphs | Algebra II | Khan Academy
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Domain of modeling functions | Functions and their graphs | Algebra II | Khan Academy


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.

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