Question

Algebra 1

Answer 1

@hartnn

Answer 2

How would you define "domain" in this situation?

Answer 3

The set of x-values

Answer 4

OR the age of service in years

Answer 5

That's a common answer, but it's not complete. Domains often (but not always) involve some restrictions on the independent (input) variable.

Look carefully at the graph. Do you see any restrictions on x?

Answer 6

I don't think so.

Answer 7

Yes, x represents "age of service in years."

Answer 8

There is no such thing as negative years as far as I know.

Answer 9

What number of subscribers would this company have at the end of year 10?

Answer 10

\[\frac{ -1 }{ 4 }(\frac{ 10 }{ 1 })^2 + 20 = -25 + 20 = -5\]

Answer 11

So, the company has a negative number of subscribers?
if the x value 7 corresponds to 2007, how many subscribers were there in 1997?

Answer 12

I don't understand.

Answer 13

By now you probably catch my drift: Values of the function for inputs other than [0,8] make no sense. The function is not defined for any x values not within [0,8].
So, you see, there are definitely restrictions on the domain of this function.

What is the domain?

Answer 14

Yes so I think that my answer is correct.
[0,8] is the interval notation of \(0 \le x \le 8\)

Answer 15

@mathmale Is that correct?

Answer 16

Very good. Next time you see the word "domain" or "range," ask yourself: Are there any restrictions? If so, what are they? Typically you'd want to express your domain and range in terms of values that x and y CAN have, but you can do the same in terms of values that are forbidden (such as (-inf, 0) ).

Answer 17

@mathmale Can you help me on a couple more questions?

Answer 18

I'd like to, but I'm about to leave on a 200-mile trip.
But I'd be happy to work with you again in the future.