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

1 Answer
Elisabeth · Stefan V.
Nov 24, 2017

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

Explanation:

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#

  • #x'# is the #x# of the function for the image
  • #b# is the variable in front of the #x# within the brackets, in this case, it would be the #-3#.
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