Question

While in the United States visiting her grandmother, Kendra copied the famous family apple pie recipe. When she returns to England, she plans on making the same apple pie for her friends. To do this, Kendra needs to convert the flour from cups to grams. She knows that 0.5 cup of flour has a mass of 64 grams and 2 cups of flour has a mass of 256 grams.

Answer 1

A. Write a function that shows grams as a function of cups. Use g(x).

B. Given this scenario, determine a reasonable domain for this function.

C.Graph the relationship between the number of cups and grams of flour.

D.Evaluate g(x) for any value of x within the domain. Interpret the meaning of your solution in the context of this problem.

E.Look at the method you used to evaluate your function in part D. Explain another way you can evaluate the function for the same input.

F.Interpret what it means to have g(-2), and determine if this is reasonable given the situation.

Answer 2

Giving medal to who can help.

Answer 3

I got A = g(x)=128x
B = 0<g<1000

I just need help with C,D,E and F.

Answer 4

Actually I think your A is incorrect. If 2 cups of flour is 256 grams, then 1 cup is 128. If you are calling grams y and cups x, you need to get y alone. But since 1x (1 cup of flour) = 128y (128 grams), you need to solve this for y (grams) in order to get the function to show grams in terms of cups. Do you see? Doing that, you get y = x/128, or 1 gram of flour is equal to 128th of a cup of flour.

Answer 5

So it's y = x/128?

Answer 6

That's what my logic dictates. The domain, then, could be any real number because she could use any amount of flour.

Answer 7

Reasonable domain might be between 0 and 2 or 0 and 3, I would guess.

Answer 8

So B's 0<g<1000?

Answer 9

The domain is your x value, which is cups.

Answer 10

A. Write a function that shows grams as a function of cups. Use g(x). that's the problem with A.

Answer 11

I need to use g(x)

Answer 12

That's fine. g(x) is the same as f(x) which is the same as y. Our g(x) axis (or y axis) is our grams and the x axis is the cups. The domain runs from side to side, or along the x axis, while the range runs up and down, or along the y axis. So domain is cups of flour. The problem tells you to write the function as grams in terms of cups, that means that grams is your g(x) or your y. So your function is g(x) = x/128. Same difference since g(x) is y.

Answer 13

Okay and B is 0<g<1000 ?

Answer 14

Why 1000?

Answer 15

Are you saying "g" as in grams? Your x axis is your domain values. Your cups are along your x axis, while your grams are along the y axis. the problem tells you that the grams needs to by your g(x) or your y, and that the cups is the x axis by elimination (if grams has to be g(x) which is y, the obviously cups has to be x). So it's an "x" in between your inequality signs, not a g.

Answer 16

So what's the reasonable domain?

Answer 17

0 and 2 or 0 and 3?

Answer 18

Like I said before, the reasonable domain, or amount of flour would probably be between 0 and 2 or 0 and 3, depending upon how many cups of flour she will need. Reasonable would probably be between 0 and 2. 0<x<2. I do not believe this has an actual "correct" answer since it is asking for reasonable.

Answer 19

Now I'm assuming you'd graph through the points (0,0)
(128,0)
(256,2)

Answer 20

MY mistake,
(0,0)
(1,128)
(2,256)

Answer 21

Then (3, 384) then (4, 512)

Answer 22

Here's C and D together since one is dependent upon the other, sort of. When you graph your function your coordinates are (.5, 64) and 2, 256). If you graph these on a plane you get a straight line. That means that for any value of x, you can find y. That translates to: for any number of cups of flour, you can find its weight in grams. The equation for this line requires you to find the slope of it using your two points and the slope formula. The equation comes out to be y = 128x. So my first thing to do is apologize because your function was correct when you said g(x) = 128x. My bad. Good for you! However, when you fill in any value for x (1.5 cups, 2.75 cups, 3.5 cups) you will solve for y and find the weight of that many cups. Do you understand how the function works?

Answer 23

Yes, btw, your coordinates above are correct.

Answer 24

Another way you can evaluate the function for the same input is to locate your x points on the graph and go up to where the y value meets it on the line. That is another way to tell how many grams (y) x cups of flour will equal.

Answer 25

That was D, btw.

Answer 26

I mean E.

Answer 27

Well, for D I put The domain could be any real number because she could use any amount of flour

Answer 28

What does it mean to have g(-2)? That means you have a negative amount of weight of flour and that is just not possible. It is not reasonable given the situation.

Answer 29

I really hope I helped you...I gotta go now! Good luck! You're doing great!

Answer 30

Is D correct?

Answer 31

And if so, I thank you a lot for the help! Hope to work with you again. Thanks :)

Answer 32

Yes, your D was correct! Good job! And thank you for the medal!