Can someone check my work please?
Eva played her favorite video game for 14 hours last week. Today, Eva;s parents restricted her to 4 additional hours each week for the next 7 weeks. Creat the function, f(x), that midles Eva's total video game time, and explain what each number in the situation graphically, using complete sentences.

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- anonymous

My function: f(x) = 14x + 7 x = 7
4 equals the y-intercept, so you would start there then go up 14 and over 1.
** I don't think my explaination is right **

- anonymous

Restricting video game time? Such injustice haha
Anyway, if she had 14 hours last week, and she gets an additional four hours every week, how many hours does she get this week? ^.^

- anonymous

Oops, I typed the function wrong. My function is... f(x) = 14x + 4 and x = 7

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- anonymous

She would get 18 hours total for one week

- anonymous

Okay, great ^^
That's 14 + 4 when the number of weeks is 1.
What about the second week?

- anonymous

She would still get 18 hours. She will get 18 hours total for every week for 7 weeks. So she'll be playing video games for 126 hours over a period of 7 weeks.

- anonymous

No, she only gets four hours each week, right?

- anonymous

I thought that she got 14 hours a week plus an additional 4

- anonymous

Yeah, I thought so too, but that's not really restricting, is it?

- anonymous

Good point... so she'll only get 4 hours for 7 weeks?

- anonymous

After you get this done, you go deal with that git that wrote this problem... doesn't know how to phrase it correctly HAHA

- anonymous

lol

- anonymous

Four hours per week, for the next seven weeks.
So, week 1, she gets 18, which is 14 + 4
.... week 2, she gets 22, right? Because she's only allowed four more hours.

- anonymous

Okay... so the function I wrote is wrong?

- anonymous

Looks like it. Incidentally, 22 is 18 + 8
or... 18 + 4(2)
See the pattern here? ^^
week 1 --> 18 + 4
week 2 --> 18 + 4(2)
week 3 --> ????

- anonymous

26?

- anonymous

Ooops... sorry, I was a too fast there.
Shouldn't be 18, should be 14.
My bad :D
week 1 --> 14 + 4
week 2 --> 14 + 4(2)
week 3 --> 14 + 4(3)
and so on, until week 7, yes? :D

- anonymous

So would the function be f(x) = 7x + 4 where x = 14 then?

- anonymous

No... x is called a variable for a reason... that's because it's the part of the equation that actually changes :D
You should keep everything else.
So in
14 + 4(1)
14 + 4(2)
14 + 4(3)
...
There's only one bit that changes... right?

- anonymous

I'm so confused on what the function would be then because my x variable can't keep changing, that's not how it works. It needs to be a number that continously makes the value increase by a certain number every single time otherwise it's not a function.

- anonymous

*continuously makes the value increase by a certain number...bla bla bla*
to increase is to change, don't you see that? ^.^

- anonymous

This is not helping ._______.

- anonymous

You need to keep an open mind here :D
14 + 4(1)
14 + 4(2)
14 + 4(3)
...obviously, the only thing that changes here is that thing you multiply to 4.
So your function should be
y = 14 + 4x
where x is the number of weeks

- anonymous

So f(x) = 4x + 14 where x = 7

- anonymous

Where x = the number of weeks that has passed -_-
For instance, after the first week, then x = 1
so the number of hours she will have played would be
14 + 4(1) or 18
which is exactly what you got earlier, right?

- anonymous

So the 7 that they put in the problem has nothing to do with function and the graph ._.

- anonymous

It does. Just not something obvious.
Technically, it means that the domain of the function is the set {0,1,2,3,4,5,6,7}
In English, it means this function only applies for up to x = 7
Which is true. The restriction imposed on the poor bloke was "only" for seven weeks.
So it's only right that we DON'T know how many hours she'll have played after eight weeks... the restriction may have been lifted or worsened by that point haha

- anonymous

Okay... so how am I supposed to graphically explain the function?
f(x) = 4x + 14 so you start the y intercept on 14 and go up 4 and over 1 until you do it seven times?

- anonymous

Yeah... only draw it until x = 7.

- anonymous

I don't have to actually draw the graph, thankfully. Just explain how it would be graphed.

- anonymous

Ahh. Okay then ^.^

- anonymous

Thank you for your help! :)

- anonymous

I'll have you know I'm like... super smart
AHAHAHAHAHAHA
Just kidding (maybe ;) )
And no problem ^.^

- anonymous

Well then, since you're super smart and all, do you mind helping me with the last problem?

- anonymous

Yes, I very much do mind. But you're going to make me do it anyway, so let's hit it HAHA

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