Question

Why does the graph translate k to the positive x direction when f(x)=(x-k)?

Answer 1

Can someone explain why for it to keep the same shape as f(x)=x it has to move in the positive direction?

Answer 2

do you can make,drawing a graph here ?

Answer 3

I dont think so but its the general transformation so...google has better drawings but i prefer someone to explain than google

Answer 4

@LanHikari22 do you can drawing it ?

Answer 5

Hmm. I have an idea on how to explain this, first, this is good to play with:
https://www.desmos.com/calculator/kmy80t5wb4
Here you go, I put different forms if you'd like seeing that.

Answer 6

Use the sliders to control the transformations.

Answer 7

One way I would try to explain why it's negative is... Think of the x axis as a time frame, like a video tape. \[F(x)=x^2\] is currently at normal configuration, if you think the vertex of x^2, or the bump, if you'd call that, the beginning of the tape, then as time goes on, the function skyrockets up, The concept of the past exists too.... the function fell down before it started raising again in the present.....

Answer 8

If you can imagine that, then start thinking what \[F(x-5)\] means. Imagine that the axes (+) the x axis, and the y axis, indicate when the PRESENT is, when the video tape starts...
so at x = 0, we're at PRESENT normally, right? the function skyrockets from there, yay! that's the very moment it launches up!!
But then what does \[F(x-5)\] mean? One way I'd interpret it is... we changed our axes! OR in other words, we start a little bit in the future. Do you know why it's in the future? Because we're looking for the new x = 0.
x-5 = 0, solve for x?
x = 5! AKA, the new axes are 5 horizontal units in the future!

Answer 9

That's how I think of it, I hope that helped.

Answer 10

@LanHikari22 nice work - !!!

Answer 11

@jhonyy9 Thank you!

Answer 12

Yes that is very helpful!
Thanks for the effort!

Answer 13

Oh also, just saying but, in the desmos page, you can replace the content of f(x) = x^2 and then just display g(x) to see the transformation. that's just a fast way to transform any function you want, I guess. Here:
https://www.desmos.com/calculator/zarknk1nbz

Answer 14

Of course, glad I was of help!

Answer 15

th value of y ( f(x)) has to be the same so if you adding k to distance x on the graph then to preserve this value you need to subtract k in the function.

Answer 16

this is not a rigorous mathematical analysis of the situation but its an easy way of remembering the method.