Transformations

Question

The base function f(x) = 1/3 is reflected in the x-axis, stretched horizontally by a factor of 2, compressed

vertically by a factor of 3 , and translated 3 units to the left and 5 units down.

1. Write the equation of this transformed function g(x).
2. Which transformations must be done first, but can be done in any order?
3. Which transformations must be done last, but can be done in any order? 

Answer 1

f(x) = 1/3 reflected about the x axis becomes f(x)=-1/3. Just change the sign

stretched horizontally changes nothing, it's still f(x) =-1/3. It's a flat, horizontal line, slope =zero, before any horizontal "stretching" and it's still the same line after "stretching.

a vertical compression by factor 3 makes the function f(x) =(1/3)(-1/3) = -1/9

shifted 3 units left changes nothing, it's still f(x) =-1/9

shifted 5 units down changes f(x) to f(x)=-1/9-5= -46/9 = g(x)

g(x)=-5 1/6 after all the transformations

Given the original order of 5 transformations, the 2nd a vertical compression has to be before the last, the shift down by 5 to get the same result, the other 2 horizontal transformations could be in any order

had the last shift come before the vertical compression

g(x) would equal (-1-5)(1/3) =-2 instead of -5 1/6

the reflection over the x axis has to come first to get the same result as the original order of transformations

the translation left and horizontal compression are irrelevant and could be done in any order, 1st, last or anytime