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

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]}