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Given #f(-3x)#, how do you describe the transformation?

Answer 1

The transformation would be reflected on the y-axis and horizontally compressed by #-(1/3)#.

This is because since the original function is #f(x)# and the transformation is #f(-3x)#, the difference is the #-3# in the brackets, which gives you two transformations to do: the reflection and the scaling.

The negative sign indicates that there is a reflection, and since it's inside the brackets, #[f(-3x)]#, it will be reflected on the #y#-axis.

The scaling of #-3# tells us that it will be a horizontal compression of #-(1/3)#, because when finding out your x values to plot and point on the graph for your transformed function (also called image), #x'=x/b#, thus the #-3# ends up at the bottom and compresses the function.

#x'=x/b#

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Answer 2

Theodore Amidon

The transformation ( f(-3x) ) describes a horizontal compression of the function ( f(x) ) by a factor of 3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.