Question

Describe how to transform the graph of f into the graph of g.

f(x) = square root x-2
g(x) = square root x+6

Answer 1

f(x-h) will translate the graph of f(x), h units to the right if h>0, and |h| units to the left if h<0.

So write \(\sqrt{x+6}\) as \(\sqrt{x-2-h}\) ... what does h=? That will tell you what you need to do with the graph of f to get the graph of g.

Answer 2

Another way to do it is to think of the x-intercepts.... what x gives you f(x)=0? What x gives you g(x)=0?

Where are those x's in relation to one another?

Answer 3

(that is more the intuitive way; the first way is more the rigorous mathematical way :)

Answer 4

Shift the graph of f left 8 units.

Answer 5

is tht the answer

Answer 6

Yes, that's it.