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Purpose of a transformed equation (in relation to matrices)

Answered

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.
E.g.
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

1 Answer

Best answer

Not quite, because the transformations affect the x and y values.

Using your x=1 and y=1 example, this is what has happened:

• dilation by factor of 2 from the y-axis has made your x=1 into x=0.5. y=1 stays the same
• reflection in x-axis makes your y=1 into y=-1. x is still x=0.5
• translation of 2 units in negative y direction makes your y=-1 into y=-3. x is still 0.5

So your x=1 and y=1 has become x=0.5 and y=-3 as a result of the transformations.

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