Transforming Function - Shifting Horizontally

[syncmaster913n]

Hello,

My problem has to do with shifting a function horizontally. I understand the how and can apply it (or at least I think so), but I don't understand why it works that way. Let me give a quick example:

Changing y = x² to y = (x+1)² shifts the graph of a function by 1 to the left. Why is that though? I mean, if we say that X is = 1, then shouldn't X just be equal to 1 on the graph no matter what, and the only thing that changes should be the value of Y? Why is the value of X changing at all? In other words, if we wanted to plot the graph of y = x² for x = [1, 2, 3], we would get:

(1, 1)
(2, 4)
(3, 9)

But then when we want to plot the graph for y = (x+1)² for the same x values ([1, 2, 3]), then why don't we just get:

(1, 4)
(2, 9)
(3, 16)

and have this represented on the graph? I'm not sure I understand where the "shift" comes from.

EDIT: funny thing, by just asking this question, I seem to have answered it for myself. Sorry for the trouble. Should I delete this post or just leave it be?

 

[Deleted member 4993]

Hello,

My problem has to do with shifting a function horizontally. I understand the how and can apply it (or at least I think so), but I don't understand why it works that way. Let me give a quick example:

Changing y = x² to y = (x+1)² shifts the graph of a function by 1 to the left. Why is that though? I mean, if we say that X is = 1, then shouldn't X just be equal to 1 on the graph no matter what, and the only thing that changes should be the value of Y? Why is the value of X changing at all? In other words, if we wanted to plot the graph of y = x² for x = [1, 2, 3], we would get:

(1, 1)
(2, 4)
(3, 9)

But then when we want to plot the graph for y = (x+1)² for the same x values ([1, 2, 3]), then why don't we just get:

(1, 4)
(2, 9)
(3, 16)

and have this represented on the graph? I'm not sure I understand where the "shift" comes from.

EDIT: funny thing, by just asking this question, I seem to have answered it for myself. Sorry for the trouble. Should I delete this post or just leave it be?

No..no ... just leave it be. May generate interesting discussion...