Moving the graph to the right -- What do you think?

  • Thread starter 0kelvin
  • Start date
  • #1
0kelvin
50
5
I'm studying calculus alone with textbooks. The part about moving the graphs to the right or to the left struck me because they just have a list of rules, properties and make you relate the graph with the corresponding equation. I know what is the rate of change and I thought I could do better than the textbook.

I vectorized this to explain why: f(x - n) moves the parabola to the right.

func_sideways.png

Not satisfied I though. f(x - 2) does remind me of the concept of a composite function. Can I draw something to explain this and relate it to the rate of change?

translation2.png
 
  • Like
Likes mcastillo356

Answers and Replies

  • #2
anuttarasammyak
Gold Member
1,843
944
With a graph described with an equation ##f(x,y)=0## given, another graph
[tex]f(x-a,y-b)=0[/tex]
is a translation of that graph with vector (a,b) on x-y plane. For an example say (0,0) is on the original graph, it is translated to (a,b) on the new one.
 
Last edited:
  • #3
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2022 Award
23,721
15,330
I'm studying calculus alone with textbooks. The part about moving the graphs to the right or to the left struck me because they just have a list of rules, properties and make you relate the graph with the corresponding equation. I know what is the rate of change and I thought I could do better than the textbook.
Take a function that is zero everywhere except the origin:$$f(x)=\begin{cases} 1 & x = 0 \\ 0 & x \ne 0 \end{cases}$$Now define ##g(x) = f(x -2)##. Note that ##g(2) = f(0) = 1##, hence:$$g(x)=\begin{cases} 1 & x = 2 \\ 0 & x \ne 2 \end{cases}$$And we see that ##g(x)## is ##f(x)## moved to the right.
 
  • Like
Likes mcastillo356
  • #4
robphy
Science Advisor
Homework Helper
Insights Author
Gold Member
6,627
2,003
Here's a related example from physics: a traveling wave disturbance on a string.

Suppose a disturbance has a profile F(x) along a string.
[In physicist's notation...]
F(x-vt) describes that disturbance translating (traveling without distortion) to the right with constant velocity v.

At t=0, consider the disturbance at the string location x=1: F(1).
After a time t, F(1)=F(x-vt) where 1=x-vt.
Since t increases, x must increase to keep x-vt=1. (Indeed, x=vt+1.)
...and similarly for other locations.
Thus, the disturbance moves to the right.

See https://www.desmos.com/calculator/bjt6dleg5h
from
https://www.physicsforums.com/threa...mean-in-the-wave-equation.836348/post-5254546
 

Suggested for: Moving the graph to the right -- What do you think?

Replies
7
Views
2K
Replies
2
Views
700
Replies
8
Views
332
Replies
23
Views
529
Replies
18
Views
353
  • Last Post
Replies
3
Views
518
Replies
2
Views
535
  • Last Post
Replies
1
Views
566
Replies
1
Views
397
Top