Which transformations to y=f(x) will produce the graphy=f(-bx) where b>1? a)A re

Question

Which transformations to y=f(x) will produce the graphy=f(-bx) where b>1? a)A reflection over the x axis, horizontal expansion byb b)A reflection over the y axis, horizontal expansion byb c)A reflection over the y axis, horizontal compression by1/b d)A reflection over the x axis, horizontal compression by1/b Which transformations to y=f(x) will produce the graphy=f(-bx) where b>1? a)A reflection over the x axis, horizontal expansion byb b)A reflection over the y axis, horizontal expansion byb c)A reflection over the y axis, horizontal compression by1/b d)A reflection over the x axis, horizontal compression by1/b

Explanation / Answer

First of all, it is easy to see that the reflection has to beover the y axis because of the negative sign inside the function. To see this, consider if x = -2, f(-x) = f(2) = 2. Hence a negative x value has a positive f(-x) value, so wehave simply flipped the line over the y axis.
If we compress the function horizontally by a factor of 3(picture this in your mind), the slope will increase to 3 and thenew function will be y = 3x. Hence the function would bef(3x). If we expand the function horizontally by a factor of3, the slope will decrease to 1/3 and the new function will bef((1/3)x). Thus we are clearly dealing with compressionhere.
In summary then, we are reflecting the function over the yaxis and compressing it, which means the answer is c.
Cheers!

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