Mathematics: Part A: Write the inputs as an ordered pair so that it is a function. Part B: Write the inputs as an ordered pair so that it is NOT a function.

Part A: Write the inputs as an ordered pair so, №11487989, 04.08.2022 00:41

Mathematics

Graham is folding a piece of paper to make an origami figure. Each time he folds the paper, the thickness of the paper is doubled. The paper starts out flat, with a thickness of 3 millimeters. A. Write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. Explain how you came up with your ordered pairs. B. Is this relation a function? Explain why or why not using the ordered pairs you came up with in Part A.

Step-by-step answer

P Answered by PhD

31

A list of ordered pairs may or may not represent a function.

The six ordered pairs are: $\mathbf{(x,y) = \{(0,3),(1,6),(2,12),(3,24),(4,48),(5,96)\}}$ .The ordered pair is a function.

(a) The ordered pair

Let x represent the number of folds, and y represent the thickness.

So, the first ordered pair is:

$\mathbf{(x,y) = (0,3)}$

When x increases by 1, the value of y gets doubled.

So, the six ordered pairs are:

$\mathbf{(x,y) = \{(0,3),(1,6),(2,12),(3,24),(4,48),(5,96)\}}$

(b) Is the ordered pair, a function

In (a), we have:

Every x value has a different corresponding y value.

This means that the ordered pair is a function.

Read more about functions and relations at:

link

Graham is folding a piece of paper to make an origami figure. Each time he folds the paper, the thic

Mathematics

George is folding a piece of paper to make an origami figure. Each time he folds the paper, the thickness of the paper is doubled. The paper starts out flat, with a thickness of 1 millimeter. A. Write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. Explain how you came up with your ordered pairs. B. Is this relation a function? Explain why or why not using the ordered pairs you came up with in Part A. (Please show work)

Step-by-step answer

P Answered by PhD

13

A) The table can be written as such:

Folds | Thickness (mm)

0 | 1

1 | 2

2 | 4

3 | 16

4 | 32

5 | 64

6 | 128

One would come to find this ordered pairs because as the paper gets folded each time, the thickness will start accumulating over time. Let's look at the first fold, now the entire paper has a thickness of 2 mm, with the next fold, we add 2 + 2 (which can be represented by 2^2) and we get 4 mm, then we fold again (4^2) and we get 8 mm and so on.

B) Yes, the relation is a function, an exponential function to be precise, since according to the amount of folds done to the paper, it will exponentially get thicker as the 1 mm stacks over and over on top of each layer.

Mathematics

Graham is folding a piece of paper to make an origami figure. Each time he folds the paper, the thickness of the paper is doubled. The paper starts out flat, with a thickness of 3 millimeters. A. Write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. Explain how you came up with your ordered pairs. B. Is this relation a function? Explain why or why not using the ordered pairs you came up with in Part A.

Step-by-step answer

P Answered by PhD

3,6,9,12,15,18

Step-by-step explanation:

How I came up with this ordered pair is taking the multiples of three this relation is a function, because it is asking to list six ordered pairs showing the output of the thickness of the paper that he folds. The way that I came up with the ordered pairs in Part A is because you have to take the multiples of three or you could just take 6 and multiple it by 3 and you would get the same answer.

And for B, this relation is not a function because the second set of numbers are not increasing by a fixed rate.

Mathematics

Jorge is folding a piece of paper to make an origami figure. each time he folds a paper, the thickness of the paper is doubled. the paper starts out flat, with a thickness of 1 millimeter. a. write a list of six ordered pairs showing the output as the thickness of the paper, when the input is the number of times it is folded. explain how you came up with your ordered pairs. b. is this relation a function? explain why or why not using the ordered pairs you came up with in part a.

Step-by-step answer

P Answered by PhD

7

If the thickness is doubled each time, this is an exponential function of the form:

t(f)=2^f, where t(f) is the thickness in mm and f is the number of fords

Some ordered pairs are (0,1), (1,2), (2,4), (3,8), (4,16) etc

Mathematics

Graham is folding a piece of paper to make an origami figure. each time he folds the paper, the thickness of the paper is doubled. the paper starts out flat, with a thickness of 3 millimeters. a. write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. explain how you came up with your ordered pairs. b. is this relation a function? explain why or why not using the ordered pairs you came up with in part a.

Step-by-step answer

P Answered by PhD

16

A.

1: 6mm

2: 12mm

3: 24mm

4: 48mm

5: 96mm

6: 192mm

By multiplying the previous thickness by 2

B.

Yes the relation is a function.

6 * 2^(x-1), where x is number of times folder.

Step-by-step explanation:

Mathematics

Royce is folding a piece of paper to make an origami figure. each time he folds the paper, the thickness of the paper is doubled. the paper starts out flat, with a thickness of 2 millimeters. a. write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. explain how you came up with your ordered pairs. b. is this relation a function? explain why or why not using the ordered pairs you came up with in part a.

Step-by-step answer

P Answered by Master

The input value is the number of times you fold it. The input value is also known as the x-value.
The output value is its thickness. The output value is the y-value.

When you don't fold it all, the thickness will remain the same, which is 2. The ordered pair would be (0, 2).

When you fold it once, the thickness will double from 2 to 4. The ordered pair would be (1,4).

When you fold it a second time, the thickness will double from 4 to 8. The ordered pair would be (2,8).

Fold it one more time, and the thickness will be 16. The ordered pair is (3,16)

Fold it the fourth time, and the thickness doubles. 16 x 2 = 32 The ordered pair is (4, 32)

Fold it the fifth time, and the thickness goes from 32 to 64. The ordered pair is (5,64)

The ordered pairs would be:
(0,2)
(1,4)
(2,8)
(3,16)
(4,32)
(5,64)
(6,128)
(7,256)
and so on :P

The question asks for 6 ordered pairs, so I bolded the first six.

Now, the equation for this would be $y = 2^{(x+1)}$

If we graph that, and we do the vertical line test, then we know this is a function.

It is a function because each x-value has a different y-value. There are no y-values that have the same x-values.

I have attached the graph of that line.
Royce is folding a piece of paper to make an origami figure. Each time he folds the paper, the thick

Royce is folding a piece of paper to make an origami figure. Each time he folds the paper, the thick

Mathematics

George is folding a piece of paper to make an origami figure. each time he folds the paper, the thickness of the paper is doubled. the paper starts out flat, with a thickness of 1 millimeter. a. write a list of six ordered pairs showing the output as the thickness of the paper when the input is the number of times it is folded. explain how you came up with your ordered pairs. b. is this relation a function? explain why or why not using the ordered pairs you came up with in part a.

Step-by-step answer

P Answered by Specialist

The input value is the number of times you fold it. the input value is also known as the x-value.
the output value is its thickness. the output value is the y-value.

when you don't fold it all, the thickness will remain the same, which is 1. the ordered pair would be (0,1).

when you fold it once, the thickness will double from 1 to 2. the ordered pair would be (1,2).

when you fold it a second time, the thickness will double from 2 to 4. the ordered pair would be (2,4).

fold it one more time, and the thickness will be 8. the ordered pair is (3,8)

fold it the fourth time, and the thickness doubles. 8 x 2 = 16. the ordered pair is (4,16)

fold it the fifth time, and the thickness goes from 16 to 32. the ordered pair is (5,32)

the ordered pairs would be:
(0,1)
(1,2)
(2,4)
(3,8)
(4,16)
(5,32)
(6,64)
(7,128)
and so on : p

the question asks for 6 ordered pairs, so i bolded the first six.

now, the equation for this would be

if we graph that, and we do the vertical line test, then we know this is a function.

it is a function because each x-value has a different y-value. there are no y-values that have the same x-values.

i have attached the graph of that line.
George is folding a piece of paper to make an origami figure. each time he folds the paper, the thic