Question

Can someone help us figure out this problem please.

Answer 1

I cannot figure out which answer it is because it seems like none of them are right?

Answer 2

\[\large y = f(x) \longrightarrow y=kf(x) \]

Answer 3

its a vertical stretch if |k| > 1

Answer 4

and here, both functions have k = 3/2

Answer 5

I thought one side is 1/2 and the other side is 1.5?

Answer 6

push 1/2 inside the abs bars

Answer 7

I totally get it now. Thanks.

Answer 8

or factor out 3 :

\[f(x) = \dfrac{1}{2}|3x-7|-2\]

\[f(x) = \dfrac{3}{2}\Big|x-\frac{7}{3}\Big|-2\]

Answer 9

this can be obtained from its parent graph \(\large y = |x|\) by doing below sequence of transformations :

1) shift Left by 7/3 units
2) vertical stretch by a factor of 3/2
3) shift down by 2 units

Answer 10

Right. Very cool. I didn't distribute the 1/2 into the absolute value signs properly at all and didn't see that it brought it to be 3/2 on both sides as a vertical stretch...

Answer 11

Take my medal away, I did this wrong!

Answer 12

haha my medals are not free ;) you deserve it lol

Answer 13

also i think the order in which we do transformations matter

Answer 14

for example :
1) left shift by 2 units
2) vertical stretch by 5 units

gives different functions when we change the order

Answer 15

So what is the rule of the order?

Answer 16

there is no rule... we can interpret a graph in many ways

Answer 17

There is no order by which we apply the translations on a function to graph it properly? I thought you just said if you change the order you get a different graph? Well which is the correct graph?

Answer 18

above is one example where the order DOESN't matter :
1) horizontal translation by m units
2) vertical translation by n units

lets see another example where the order matters, and where we can interpret the graph in several ways depending on the order in which we do the transofrmaiton

Answer 19

Aiight

Answer 20

y = 2|x-3| + 2

this can be interpreted in atleast two different ways.

First :
1) shift right by 3 units
2) vertical stretch by 2 units
3) shift UP by `2` units

Second :
1) shift right by 3 units
2) shift UP by `1` unit
3) vertical stretch by 2 units

Answer 21

Notice that, both sequence of transformations are referring to the same graph,
but if you change the order, you will get a different graph.

Answer 22

Right... so which is the real graph?

Answer 23

what do you mean by a real graph -
First, and Second sequence of transformations lead you to SAME graph

Answer 24

just two different ways of interpreting the same graph

Answer 25

yes I am going to say that next

Answer 26

Sorry! Please say it >_<

Answer 27

change the order in First sequence. you will get a different graph.

First(NOT same) :
1) shift right by 3 units
3) shift UP by 2 units
2) vertical stretch by 2 units

Answer 28

I have swapped 2) and 3) steps -
this produces a different graph

Answer 29

Wait.. so the order does make different graphs... -_-

Answer 30

Exactly ! if you simply change the order, you will get different graphs most of the time.

Notice that in the First and Second sequence of transformations which we did earlier, we changed both the order and also `the individual transformation` - thats the reason, both are referring to the same graph

Answer 31

So back to my original question. How do we know which order to apply the operations so we come to the correct graph in the end?

Answer 32

again it doesn't matter - when u change the order, you will be changing the individual transformation also.

Answer 33

y = 2|x-3| + 2

this can be interpreted in atleast two different ways.

First :
1) shift right by 3 units
2) vertical stretch by 2 units
3) shift UP by 2 units

Second :
1) shift right by 3 units
2) shift UP by 1 unit
3) vertical stretch by 2 units

Answer 34

Both are correct ways of interpreting the given transformation. Notice that the `shift UP` is not same in both the interpretations

Answer 35

You are driving me batty @ganeshie8.

Answer 36

ikr..

Answer 37

Lol

Answer 38

Ok, stick with me here. I totally get that the order that we apply the operations yields different graphs in the end. But only one of the graphs will be correct. Right?

Answer 39

let me put it like this :

I have x :
1) add 3 : x+3
2) multiply 5 : (x+3)*5

Answer 40

So far so good

Answer 41

now change the order in which you performed things :

I have x :
2) multiply 5 : 5x
1) add 3 : 5x+3

Answer 42

thats the only thing i have been failing to say o,o