Odd thing about dilations... (1 Viewer)

[Aerlinn]

For any graph, are dilations supposed to affect translations? When I consider it, they shouldn't, not all the time at least...
eg. The simplest graph I can think of, y=(3x+1)^2 vs y=(x+1)^2... You'd think that as dilations are done first, you dilate (the 3), and the graph shouldn't move from where it's sitting on that spot on the x-axis, then it's translated, but it's translated -1/3 units, less than the second graph. Why does the dilation affect the translation?

 

[pLuvia]

If you were going to draw the first graph it would be much steeper than the second graph. You draw the graph at the same time (for those examples at least)

I'm not sure what you are getting at here. If you dilate something it either contracts or widens and this won't affect translating the graph since you are translating it with a constant

 

[jyu]

For any graph, are dilations supposed to affect translations? When I consider it, they shouldn't, not all the time at least...
eg. The simplest graph I can think of, y=(3x+1)^2 vs y=(x+1)^2... You'd think that as dilations are done first, you dilate (the 3), and the graph shouldn't move from where it's sitting on that spot on the x-axis, then it's translated, but it's translated -1/3 units, less than the second graph. Why does the dilation affect the translation?

I think you confused y=(3x+1)^2 with y=[3(x+1)]^2.
The latter represents horizontal dilation of y=x^2 by a factor of 1/3.
y=(x+1)^2 is the translation of y=x^2 to the left by 1 unit and y=[3(x+1)]^2 is the translation of y=3x^2 to the left by the same amount.
So dilation does not affect translation.

For y=(3x+1)^2=[3(x+1/3)]^2, it represents horizontal dilation of y=x^2 by a factor of 1/3 and then translation of y=3x^2 to the left by 1/3.

 

[Aerlinn]

I think I get ya. You're saying we shouldn't compare y=(3x+1)^2 and y=(x+1)^2 because they're translated different amounts anyway? Yes I'd been wondering for a while why, when you pop in a dilation factor of 1/3 (the 3), it suddenly gets translated not 1 unit but 1/3.