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

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In summary, the conversation discusses the concept of moving graphs in calculus and the role of equations in relating them. The idea of translating a function with a vector is explained, as well as an example of a traveling wave disturbance on a string. The concept of a composite function is also mentioned in relation to translating graphs. The conversation highlights the importance of understanding these concepts in order to have a deeper understanding of calculus.
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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
 
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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.
 
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0kelvin said:
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.
 
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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
 

1. How does moving the graph to the right affect the data?

Moving the graph to the right shifts all the data points to the right, meaning that the x-values will increase while the y-values remain the same. This results in a horizontal translation of the graph.

2. Why would you want to move the graph to the right?

Moving the graph to the right can be useful for displaying data that has a larger range of values on the x-axis. It can also help to highlight specific data points or trends in the data.

3. Does moving the graph to the right change the shape of the graph?

No, moving the graph to the right only changes the position of the data points. The shape of the graph remains the same.

4. How do you move the graph to the right?

To move the graph to the right, you can add a constant value to all the x-values in the data set. This will shift the graph to the right by that amount.

5. Can moving the graph to the right affect the accuracy of the data?

No, moving the graph to the right does not affect the accuracy of the data. It only changes the position of the data points on the graph.

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