Question

Given that (4,6) is on the graph of f(x), find the corresponding point for the function f(-4x)

Answer 1

well what do you think is the answer.

Answer 2

I'm just wondering how to do it. Like I know that f(x) - 4 would move the point right by 4, and vice versa for f(x) + 4, but idk what to do in f(-4x)

Answer 3

@3mar do you know?

Answer 4

well if you were to put f(-4x) in it would come out as -4fx

Answer 5

NO....the right analysis is:
- f(x) - 4 would move the point DOWN by 4 units
- f(x) + 4 would move the point UP by 4 units
- f(x-4) would move the point to the RIGHT by 4 units
- f(x+4) would move the point to the LEFT by 4 units

Answer 6

yeah. thats right.

Answer 7

sorry, yes. I got confused as I was typing

Answer 8

what would we do without u to help guide us, @3mar

Answer 9

But our case is not included, and it includes two things:
1. the function is enlarged FOUR times \(f(4x)\)
2. the function is reflected about the y-axis \(f(-x)\)
------------------------------------
the resultant function is \(f(-4x)\) reflected about the y-axis and magnified\enlarged/multiplied by \(\LARGE 4\)

So the rule would be:
\[\Huge (x,y) \rightarrow (\color{red}{-4}x, f(\color{red}{-4}x))\]

Answer 10

But I want to ask you a question @ElizaBethBOB
WHERE is the function rule of f(x)?

Answer 11

but if you take the (x,y)->(-4x,f(-4x) it is -4fx

Answer 12

It is not a condition @Gluttrell

Answer 13

I still don't understand how to calculate the new point, do I multiply -4 and 6?

Answer 14

yes

Answer 15

WHERE is the function rule of f(x)?
It must be given.
or at least the graph of the function f(x)...

Answer 16

It's only giving me the point (4, 6) and the function f(-4x)

Answer 17

but u already knew that didn't you love_to_love _you, you just needed to verify it.

Answer 18

Yes, I just want to understand it correctly because I'm confused

Answer 19

CORRECTION
\[\Huge (x,y) \rightarrow (\color{red}{}x, f(\color{red}{-4}x))\]
- reflection about y-axis
- magnified by a factor of of \(\Large 4\)


so what you should to do is:
- multiply 6 by 4.
- negate the result.

Answer 20

so the new point would be (4, -24)?

Answer 21

Excellent!
but there is one point"""
as we reflect the function about the y-axis, the x-coordinate will be negated....


**Reflection across y-axis: (x,y) > (-x, y)

Answer 22

So the point will be \(\Huge (-4,-24)\)

Answer 23

Oh, okay! Thank you @3mar

Answer 24

Don't mention it!
You are welcome!

BUT Are you persuaded?

Answer 25

Yes

Answer 26

I am happy to hear that...and that what matters...

Answer 27

Thank you for learning!

Answer 28

Thank you for teaching me!

Answer 29

Thank you for your appreciation!
Thank you for your confidence.
Thank you for the medal!
I thank you for giving me that chance to help you!