Question 1066486
here's a good reference on transformations.
<a href = "http://cms.cerritos.edu/uploads/pmata/Math%20140%20Materials/Chapter%201/1.7_Transformations.pdf" target = "_blank">http://cms.cerritos.edu/uploads/pmata/Math%20140%20Materials/Chapter%201/1.7_Transformations.pdf</a>



your equation is y = sqrt(x).


it is shown below with check points at x = 4 and x = 16.


<img src = "http://theo.x10hosting.com/2017/020502.jpg" alt="$$$" </>


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.


<img src = "http://theo.x10hosting.com/2017/020503.jpg" alt="$$$" </>


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.


<img src = "http://theo.x10hosting.com/2017/020504.jpg" alt="$$$" </>


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.


<img src = "http://theo.x10hosting.com/2017/020505.jpg" alt="$$$" </>



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.