# How do the graphs of f(x)=sqrtx+2 and g(x)=sqrt(x+2) compare?

Jan 22, 2018

See below.

#### Explanation:

graph{sqrt(x)-2 [-10, 10, -5, 5]}

For $\sqrt{x} - 2$, above.

graph{sqrt(x-2) [-10, 10, -5, 5]}

For $\sqrt{x - 2}$, above.

They are pretty similar, for one fact: doing $f \left(x\right) - k$ shifts the graph $k$ units down, and $f \left(x\right) + k$ shifts it $k$ units up.

On the other hand, doing $f \left(x - k\right)$ shifts the graph $k$ units right, and $f \left(x + k\right)$ shifts it $k$ units left.

And so, the above.