Question 1066486: Let f(x) = √x. Write the equation for the final transformed graph if the following
transformations are applied to f, in the following order: stretch horizontally by a factor
of 2; shift downward by 5 units; shift right by 3 units.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's a good reference on transformations.
http://cms.cerritos.edu/uploads/pmata/Math%20140%20Materials/Chapter%201/1.7_Transformations.pdf
your equation is y = sqrt(x).
it is shown below with check points at x = 4 and x = 16.
it will be easier to see the transformations if we stretch it first.
your stretched equation is y = sqrt(x/2)
it is shown below with check points at x = 8 and x = 32.
your stretched equation shifted down 5 units is y = sqrt(x/2)-5.
it is shown below with check points at x = 8 and x = 32.
your stretched equation shifgted down 5 units and then shifter right 3 units is y = sqrt((x-3)/2)-5
it is shown below with check points at x = 11 and x = 35.
the original checkpoints are at x = 4 and x = 16.
when x = 4,sqrt(x) = 2
when x = 16, sqrt(x) = 4
when you stretch it by a factor of 2, the checkpoints becomes x = 8 and x = 32.
when x = 8, sqrt(x) = 2
when x = 32, sqrt(x) = 4
when you shift it down by 5, the check points remain at x = 8 and x = 32.
when x = 8, sqrt(x) = 2 - 5 = -3
when x = 32, sqrt(x) = 4 - 5 = -1
when you shift it to the right by 3 units, the check points become x = 11 and x = 35.
when x = 11, sqrt(x) = -3.
when x = 35, sqrt(x) = -1.
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