How do you write and graph a function that translates #y=sqrtx# by shifting 5 units right and 3 units up?

1 Answer
Jun 6, 2017

#y=3+sqrt(x-5)#

graph{sqrt(x-5) +3 [-10, 10, -5, 5]}

Explanation:

The function #y=sqrt(x)# looks like this:

graph{sqrt(x) [-10, 10, -5, 5]}

Shifting the function 5 units to the right means translating the function 5 units along the x-axis. So we will subtract #5# from #x#.

#y=sqrt(x-5)#

graph{sqrt(x-5) [-10, 10, -5, 5]}

Add 3 to shift the function 3 units up:

#y=3+sqrt(x-5)#

graph{sqrt(x-5) +3 [-10, 10, -5, 5]}