Question

the ordered pair (0,0)(1,4)(2,16)(3,36)(4,64). write a rule that represents the function.

Answer 1

what I had made sense until I reached the part where it said (3,36) and (4,64)

Answer 2

What do you notice about the y-coordinates for each ordered pair?

Answer 3

it multiplys by 2s

Answer 4

I'm guessng the 4th one is not correct. Should be (3,32)

Answer 5

yeah i got confused by that one

Answer 6

No.

Let's look at the y-coordinates:

0, 4, 16, 36, 64

Anything interesting about these numbers?

Answer 7

multiples of 4

Answer 8

Sry my bad

Answer 9

I got confused because of the answer I had before

Answer 10

So what do you think the function should be hannah?

Answer 11

I htought it was 4x^2

Answer 12

thought*

Answer 13

Are they multiple of 4 in any order? No.

Multiples of 4: {4,8,12,16,20,24,28,...}

So those numbers are a subset (part of) the set oif multiples of 4.

Try again...what is common to all those y-coordinate numbers ?

Answer 14

want a hint?

Answer 15

yes

Answer 16

They are all perfect squares.

But the question is, what pattern do these perfect squares form?

Answer 17

2,4,6,and 8

Answer 18

I assume mean,

0^2 = 0
2^2 = 4
4^2 = 16
6^2 = 36
8^2 = 64

So what exactly is the pattern???

Answer 19

Notice the y-coordinates are 0,4,16,36,64, ....

Answer 20

they all have an exponent of 2?

Answer 21

well, yes, that's what we mean by a perfect square.

To see if you understand the pattern,
what will be the coordinates of the point AFTER (4,64)?

Answer 22

(5,81)?

Answer 23

No. Try again.

Answer 24

sadly idk T_T

Answer 25

try getting y-coordinate as function of the x-coordinate

Answer 26

0^2 = 0 ;2^2 = 4 ; 4^2 = 16; 6^2 = 36; 8^2 = 64

If you notice that it skips by 2, 0^2, then 4^2, then 6^2, then 8^2, so I expect the the next coordinate would be (5,100)...Would you agree?

Answer 27

Oh now I understand

Answer 28

First y - coordinate is: 0^2
Second y-coordinate is: 2^2
Third y-coordinate is: 4^2
Fourth y-coordinate is: 6^2
Fifth y-coordinate is: 8^2
Sixth y-coordinate is: ???????

Answer 29

Sith y-coordinate is: 10^2

So what would be the Seventh y-coordinate?

Answer 30

12^2

Answer 31

Exactly!

Answer 32

Now, let's try to get a rule that generates the coordinates. That was your original question.

Can you give me the rule?

Answer 33

the the rule to represent the function

Answer 34

Yes, we are looking for a rule that relates y with x.

Look at the x-coordinates and the y-coordinates. How are they related?

Answer 35

I can see how they are related separatly but not together.

Answer 36

Try looking at it again for a moment or two...see if you can see how they are related together.........

Answer 37

1*4=4 2*8=16 3*12=36 4*16=64

Answer 38

very interesting.....

Answer 39

so how would you write your rule, like y = something with x

Answer 40

4*1^2=4 4*2^2=16 4*3^2=36 now just express it with x instead of numbers

Answer 41

I was looking at the rule from a different angle..with perfect squares

Answer 42

@HannahKimiko

So what would be the rule?

Answer 43

4x^2?

Answer 44

exactly

Answer 45

Now what do you think the pair should be ?

Answer 46

Nice job, @HannahKimiko

So what is the rule? Let's write it mathematically as an ordered pair (x,y)?

Answer 47

y=4x^2?

Answer 48

Yes, thats perfect...as the question just asks for the rule as a function, and y = 4x^2 is a function of x.

Answer 49

Yay!!!!!!!!

Answer 50

And, by the way, since we have the rule...we can easily figure out any coordinate...say when x = 20, then y = 4(20^2) = 4(400) = 1,600.

Answer 51

thats's interesting ^^

Answer 52

@HannahKimiko

Now, whenever you see such a question, try to see the pattern, and relate that pattern with x, to develop a function rule.

Answer 53

how do you do one with fractions though?

Answer 54

Sometimes you do find questions...where they give you a certain pattern, and will ask, "What would be the 10th term, etc..". That's easy once you have the rule.

Answer 55

Well, the same way with fractions...if you have an exercise like this one that contains fractions, we can look at that if you want.

Answer 56

um... (1,2/3) (2,4/9)(3,8/27)(4,16/81)(5,32/243)

Answer 57

OK..take a few moments and see if you can first establish a pattern.

Answer 58

can you change it to a decimal?

Answer 59

Dont change into a decimal...look at these fractions

2/3, 4/9, 8/27, 16/81, ...

anything seem interesting about these numbers?

Answer 60

the denominator is a multiple of 3

Answer 61

and the numerator is a multiple of 2

Answer 62

so look at the first 2 numbers, 2/3 and 4/9...how are they related?

Answer 63

it's simplified

Answer 64

Oh yea? When you simplify 4/9, you get 2/3?

Answer 65

How so?

Answer 66

oops lol

Answer 67

Hint:

First term, 2/3 = (2/3)^1
Second term, 4/9 = (2/3)^2

Do you see the pattern now?

Answer 68

yeah

Answer 69

So what is the function rule that relates y with x?

Answer 70

y = ?

Answer 71

y=2/3^2

Answer 72

I dont see y in terms of x

Answer 73

y=2/3^x

Answer 74

First term: y = (2/3)^1
Second term: = = (2/3)^2
Third term: y = (2/3)^3

So the general rule is what? y = what?

Answer 75

Yes, y = (2/3)^x. Perfect!

So you're getting the hang of it. Just practice, and you'll do fine. If you need more help, write back.

Answer 76

can you give me a hint?

Answer 77

oh lol

Answer 78

i htought i got it wrong

Answer 79

okay thank you

Answer 80

You can see that it is correct.

How?

Take the 4th term, is the fourth term y = (2/3)^4?
(2/3)^4 = 16/81..so it checks.

Answer 81

And you can find any term, once you know the rule.

Answer 82

@HannahKimiko

You're welcome.

Answer 83

for the ordered paris (1,2)(2,16)(3,54)(4,128)(5,250) the function is y=2x^3, right?

Answer 84

Yes!

Answer 85

what do you do when the numbers are increasing and decreasing?

Answer 86

likr the pattern is (0,0) (1,.5)(2,2)(3,4.5)(4,8)

Answer 87

You may need X+1 or x-1, etc...

Answer 88

Oh okay

Answer 89

can you help me with this one?

Answer 90

The last one you typed is an interesting one.

Answer 91

Try writing a rule for that.

Answer 92

First, study the pattern, and see if you "can see" ther pattern. Once you see the pattern, write the rule.

Answer 93

i got you add.5 the 1.5 each time after that.....?

Answer 94

agree...and then you multiply that by x.

Answer 95

Now, you must relate y with x, and write a rule. And use the rule to check if that rule works for the given coordinates.

Answer 96

I will leave that for you to do.

Answer 97

I will leave that for you to do.