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

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Answer 1 · 2018-01-22T14:03:35

See below.

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(x)-k# shifts the graph #k# units down, and #f(x)+k# shifts it #k# units up.

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

And so, the above.