Question

so If I have a point (0,2) on the function f(x)
where would that point be in the transformation
f(2(x-2))?

Answer 1

I had this in a precalc test so I want to know if I did it correctly

Answer 2

Are you sure you need my help @darkknight? You seem to understand math fairly well already.

Answer 3

pretty sure

Answer 4

need assurance for pre-calc

Answer 5

I see. There's a way you can check this yourself. Here's what you can do. Graph an expression in desmos that includes the point of interest. Name it \(f(x)\). Then apply the rule \(f(2(x-2))\) to see where the point transforms to.

Answer 6

okay

Answer 7

That should give you some intuition as to how the transformation \(f(2(x - 2))\) works.

Answer 8

but if a I had a function that effects the graph vertically, like if I had -3f(2(x-2))+5, then I couldn't use desmos. What would I do then

Answer 9

also including like other points

Answer 10

I think 3,7 was one and 9,3 was another

Answer 11

Why do you assume you are unable to use desmos?

Answer 12

You could find the equation of the line including the two points, name that \(f(x)\) then apply the transformation.

Answer 13

because then I wouldn't know the individual points. Like I wouldn't know where 0,2) is then

Answer 14

Not following what you mean. You know the location of \((0,2)\). Its two units north of the origin.

Answer 15

what I mean is that when 0,2) is applied in the transformed version. It is a different point. different x and y coordinates. so I wouldn't know where the point 0,2 is then

Answer 16

So I don't think I can use desmos

Answer 17

wait a minute

Answer 18

so in -3f(2(x-2))+5, 0,2 turns to be 2,7?

Answer 19

because the point is shifted 2 to the right and 5 up?

Answer 20

That is obviously incorrect because the negative implies that at some point you flip the point over the x-axis.

Answer 21

okay thats good, because thats not what I did on the quiz, lol

Answer 22

so this is what I did on the quiz

Answer 23

what happened

Answer 24

well I'll restart

Answer 25

So for the point (0,2) I would plug in 0 for x. subtract by 2 then multiply because inside the parenthesis is where the x is effected. I would then take the 2 and multiply by -3, then add 5. I would do something similar for the other ones

Answer 26

I don't know if thats right though

Answer 27

like how would you transform (0,2) @hero

Answer 28

someone plz help

Answer 29

I got -4,-11 for 0,2

Answer 30

How did you end up with that? Explain.

Answer 31

its up there

Answer 32

I must have said something that confused you.

Answer 33

Or maybe that was one of your answer choices.

Answer 34

we have no answer choices

Answer 35

if you apply the transformations to the point 0,2 do you end up with -4,-11?

Answer 36

Well, I have a method for doing these. It's unconventional but it gets the correct result.

Answer 37

how do you do it?

Answer 38

I want to know

Answer 39

@Hero?

Answer 40

To avoid confusing yourself, you should just follow the way your book teaches it.

Answer 41

well my book literally doesn't teach this

Answer 42

it only talks about transformations of functions not about individual points

Answer 43

how do you do it? I won't be confused. As long as it doesn't involve calculus or something

Answer 44

brb

Answer 45

please post your method though

Answer 46

Sorry if you felt I abandoned you. I was trying to think of an easier way to explain it.

Answer 47

Which I have now.

Answer 48

okay

Answer 49

So we have the point \((0,2)\) and we have to move it by the transformation \(-3f(2(x - 2))+5)\)

Answer 50

Since we know that \((0,2)\) is on the graph of \(f(x)\) we can say \(f(0) = 2\)

Answer 51

This means that for our transformation we need to make \(2(x - 2)\) = 0

Answer 52

why equals 0?

Answer 53

When we do this we find that the \(x-\) coordinate of our transformed point is \(x = 2\)

Answer 54

I don't get why 2(x-2) =0
like why 0?

Answer 55

nvm I get it

Answer 56

go on

Answer 57

Now that we know the \(x\) value, we set up the transformation this way:

Answer 58

\(-3f(2(2-2))+5\)

Answer 59

And that simplifies to \(-3f(0) + 5\)

Answer 60

hold up

Answer 61

nvm

Answer 62

But since \(f(0) = 2\) we can write \(-3(2) + 5\)

Answer 63

Continue simplifying to get the y coordinate.

Answer 64

okay

Answer 65

well I definetly failed the quiz lol

Answer 66

So you now know the transformed point is \((2, -1)\)

Answer 67

I hope you at least understand how to do these now.

Answer 68

thanks

Answer 69

the hero

Answer 70

There's another method of this that is not easy to explain.

Answer 71

okay, I have to go

Answer 72

Maybe that other explanation is what confused you.

Answer 73

thanks though

Answer 74

what about the point 3,7?