Find the function that is finally graphed after the followin

Find the function that is finally graphed after the following transformations are applied to the graph of y = sqrt x


i) Shift up 9 units
ii) Reflect about the x-axis
iii) Shift right 5 units

Solution

y= sqrt(x)

i) If the graph shift up by 9 units then we need to add 9 to the function , hence we got

y= sqrt(x) +9

ii) Now graph relect about the x axis , hence we have

y= -sqrt(x) +9

iii) Graph shift right by 5 units , hence we have

y= -sqrt(x-5) +9

Therefore the graph we will get after the above transformation is

y= -sqrt(x-5) +9