general graph transformation

need help in this question ( will upload question after a sec)
as i am confused about part c
y=-f(x)+4

as there any rule which transformation should i do before and which do after
if i do the transformation of +4 ( move up 4 units) and then do -(fx)
it will give points
-2,-4
-1,-8
0,-7 i try to show in the graph ( top corner)

and if i do -f(x) first and then +4 it will give points
-1,0
0,1

why ? what i am doing wrong?/

@RDKGames
@Desmos

(edited 6 years ago)

Reply 3

MR1999

I would say do -f(x) first and then +4, but you should wait for a reply from @RDKGames, @Notnek or @Zacken.

(edited 6 years ago)

Reply 4

Zacken

Original post by Desmos

I would say do -f(x) first and then +4, but you should wait for a reply from @RDKGames, @Notnek or @Zacken.

You're correct

@OP, if you do +4 first you go from f(x) to g(x) = f(x) + 4 then (-1) gives h(x) = -4 - f(x) which is a different thing

Reply 5

MR1999

Original post by Zacken

You're correct

@OP, if you do +4 first you go from f(x) to g(x) = f(x) + 4 then (-1) gives h(x) = -4 - f(x) which is a different thing

OP, this may confuse you, so I would recommend you don't read this.

But does

-f(x)+4 = -(f(x)-4)?

Reply 6

Zacken

Original post by Desmos

OP, this may confuse you, so I would recommend you don't read this.

But does

-f(x)+4 = -(f(x)-4)?

Yes

Reply 7

Qer

Original post by Zacken

You're correct

@OP, if you do +4 first you go from f(x) to g(x) = f(x) + 4 then (-1) gives h(x) = -4 - f(x) which is a different thing

1. Translation in x f(x+a)
2. Stretch in x f(ax)
3. Reflect in x -af(x)
4. Reflect in y f(-ax)
5. Stretch in y af(x)
6. Translate in y f(x)+a

@Desmos

is that order id fine???

Reply 8

MR1999

Original post by Zacken

You're correct

@OP, if you do +4 first you go from f(x) to g(x) = f(x) + 4 then (-1) gives h(x) = -4 - f(x) which is a different thing

@Qer if Zacken's explanation confuses you, here's another way to look at it:

let f(x) = y
then -f(x) + 4 = -y + 4

But if we did +4 first, this is what happens:

y → y+4 → -(y + 4) = -y - 4 = -f(x) - 4: Not what we were looking for

Reply 9

MR1999

Original post by Qer

1. Translation in x f(x+a)
2. Stretch in x f(ax)
3. Reflect in x -af(x)
4. Reflect in y f(-ax)
5. Stretch in y af(x)
6. Translate in y f(x)+a

@Desmos

is that order id fine???

The order of operations should suffice.

Reply 10

Qer

I x -a I means both x and a are positive

so x+a =0
then x=-a???

Reply 11

Zacken

Original post by Qer

I x -a I means both x and a are positive

No it doesn't

so x+a =0

No?

|b| = 0

if and only if

b=0

. So

|x-a| = 0

if and only if

x-a = 0

Reply 12

MR1999

Original post by Qer

I x -a I means both x and a are positive

so x+a =0
then x=-a???

|x-a| means that whatever is between the || now becomes non-negative.

Reply 13

Qer

Original post by Desmos

|x-a| means that whatever is between the || now becomes non-negative.

This is what I am saying
Isn't it?

Reply 14

RDKGames

Study Forum Helper

Original post by Qer

This is what I am saying
Isn't it?

No. You are saying that

x \geq 0

and

a \geq 0

which is not what

|x-a|

means

Reply 15

Qer

did i need to know how to find value of a reciprocal function without using a calculator for c3?? because Edexcel book have questions to find values without using calculator

like sec240??

Reply 16

MR1999

Original post by Qer

This is what I am saying
Isn't it?

It becomes non-negative because the sign of whatever's inside changes if it's negative. So

|2-5|=3

Reply 17

RDKGames

Study Forum Helper

Original post by Qer

did i need to know how to find value of a reciprocal function without using a calculator for c3?? because Edexcel book have questions to find values without using calculator

like sec240??

No. How would they know whether you have used a calc or not if you are allowed to use a calc on the paper...?