Function Rules

[Prentice]

Hello. Can you help me please? I am having a problem with functions. I get writing rules for linear functions, but I don't get the function rules for situations like these ones.

Write a rule that expresses the number of quarts Q of a liquid as a function of each of the following

a. the number of pints p

b. the number of fluid ounces f

Thanks for any explanations you can give me. I got the answers from a friend but I don't get it. Here are the answers.

a. q(p)= 1/2 p

b. q (f) = f/32

 

[Gene]

You have to know there are
2 pints to 1 quart and
32 oz to 1 quart.
so
q=(1/2)p and
q=(1/32)f
You can check them by putting in 2 pints and 32 fl oz in the respective formulas and seeing that the answers are both 1 q.

 

[Prentice]

But why isn't it q=2p instead? I guess I don't get functions as much as I thought.

 

[stapel]

But why isn't it q=2p instead?

When you're not sure with the variables, try it with numbers instead: If you have, say, two pints, do you then have 2(2) = 4 quarts?

Eliz.

 

[Gene]

One more response, then I'll write you off as a troll.
If you use your formula and (as I said) you use p = 2 you are saying you get 4 quarts.
q = 2p = 2*2 = 4 qts.
That's why it is wrong.
With
q = p/2
if you use p = 2 we are saying you get 2/2 = 1 quart
2 pints = 1 quart.
-----------------
Gene

 

[Prentice]

OK, thanks.

I just need to go back and revisit the concept, obviously. I'm not sure why someone would say I was a troll, but whatever. I appreciate the responses.

 

[Gracie]

Prentice,

The formula q(p) is saying what are your quarts in terms of pints. Since they are asking for your formula in terms of pints then you need to calculate the quarts in terms of pints. if you have 2 pints, then you would have 1 quart so your quarts are 1/2 of your pint count.

q(p) = 1/2 (p)

If I gave you the number of quarts then you could multiply by 2 and get the number of pints and that would be p(q) = 2 (q).

so basically you need to divide and not multiply to get from pints to quarts thus:

q(p) = 1/2 (p) (since multiplying by 1/2 is the same as dividing by 2).

In linear functions like this one, you have pints as your control variable (x veriable) and quarts as your dependent variable. (y term).

 

[stapel]

I'm not sure why someone would say I was a troll....

Sorry 'bout that. "Tis the season", I'm afraid. We've been getting a lot of, well, unpleasant posts, some actual trolls, others just bums wanting tutors to do their online tests for them, or write up their homework for them, or whatever.

I apologize: I think "happy" maybe jumped a little too quick in this case. Comin' down from the 'nog, maybe...?

Eliz.

 

[Gene]

Ah ah ah, Eliz. Credit (or blame) where due. Not Happy but Gene. While it is possible my reply was just not read when I have said

You can check them by putting in 2 pints ... in the ... formula and seeing that the answer [is] 1 q

And the next query is "why not 2p" it seems that it has to be one or the other. I would rather be thought a troll than an illiterate :evil:
---------------
Gene

 

[Prentice]

Thanks, everyone, especially Gracie.

I like the way you explained the pints and quarts and I get that and I copied it off to put in my notebook. Being called illiterate isn't too nice, but I guess it was worth it to get a good explanation. Thank you again.