Say for example I had the equation y = x^3
They go through the following transformations
. dilation by a factor of 2 from the y-axis
. reflection in the x-axis
. translation of 2 units in the negative y direction
The resulting transformed equation is y= -(x/2)^3 - 2
Does this mean that, for any point on the graph of the original function, y=x^3, we could determine the corresponding point under the transformations above by substituting the same values into this transformed equation.
If I subbed in x = 1 into y=x^3 I'd get y=1
If I subbed in x = 1 into y= -(x/2)^3 - 2 I'd get y= -2.125
This essentially means that the y value moved from 1 to -2.125 due to the transformations that occurred
if i were to use x=1 as my reference.
Is this how I would interpret what a transformed equation does? Thanks