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

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Answer 1 · 2017-06-06T16:51:11

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

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

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]}