Say for example we have f(x) = |x|, and we need to find the image of the graph after it undergoes the following transformations (in this order).
- a dilation of factor 2 from the x axis
- a reflection in the x axis
- translation of 3 units in the positive direction of the x axis
- translation of 4 units in the negative direction of the y axis
so (x,y) -> (x, 2y) -> (x, -2y) -> (x+3, -2y-4)
now x' = x+3
and y' = -2y-4
My question is why do we have to rearrange and solve for x and y before substituting back into y = |x|?
Our teacher never really explained why you can't just plug in x+3 for x and -2y-4 for y, and instead would have to use x-3 and -y/2 -2 respectively.
Muchly appreciated
- a dilation of factor 2 from the x axis
- a reflection in the x axis
- translation of 3 units in the positive direction of the x axis
- translation of 4 units in the negative direction of the y axis
so (x,y) -> (x, 2y) -> (x, -2y) -> (x+3, -2y-4)
now x' = x+3
and y' = -2y-4
My question is why do we have to rearrange and solve for x and y before substituting back into y = |x|?
Our teacher never really explained why you can't just plug in x+3 for x and -2y-4 for y, and instead would have to use x-3 and -y/2 -2 respectively.
Muchly appreciated