Q: For each of the following, find a sequence of transformations that takes \(\displaystyle y\, =\, x^2\) to \(\displaystyle y\, =\, (2x\, +\, 1)^2\, -\, 2\)
By what I understand about transformations, there's 4 main ones:
We move -2 from the right side to the left side
Making it y' + 2 = (2x' + 1)2
This makes it Y = Y' + 2 & X = 2x' + 1
Now, Solving for Y' and x'
Y' = Y - 2
X' = (X - 1)/2
Now, to put it in words - A transformation is a dilation of 1 from Y axis, then a translation of 1/2 unit in the negative direction of the x-axis and 2 units in the negative direction of the Y-axis.
Is this correct guys? My answers say it's a dilation of a factor of 1/2 from the y axis... I don't get why..
By what I understand about transformations, there's 4 main ones:
- Translation
- Dilation
- Reflection
- Rotation
We move -2 from the right side to the left side
Making it y' + 2 = (2x' + 1)2
This makes it Y = Y' + 2 & X = 2x' + 1
Now, Solving for Y' and x'
Y' = Y - 2
X' = (X - 1)/2
Now, to put it in words - A transformation is a dilation of 1 from Y axis, then a translation of 1/2 unit in the negative direction of the x-axis and 2 units in the negative direction of the Y-axis.
Is this correct guys? My answers say it's a dilation of a factor of 1/2 from the y axis... I don't get why..
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