Question

What transformation can you apply to `y=sqrtx` to obtain the graph `y=sqrt(2(x+3))+1`?

Answer 1

See explanation.

Explanation:

Successive transformations:

(0) `y = sqrtx`

(1) `y = sqrtx + 1`, by ( linear transformation of ) subtracting 1 from y

(2) `y = sqrt(2x)+1`, by applying the ( scaling ) factor 2 to x.

(3) `y = sqrt(2(x+3)+1`, by ( linear transfor mation of ) adding 3 to x

The successive graphs illustrate the successive transformations,

respectively

graph{sqrtx [-10, 10, -5, 5]}

Graph-0

graph{sqrtx+1 [-10, 10, -5, 5]}

Graph-1

graph{sqrt(2x)+1 [-10, 10, -5, 5]}

Graph-2

graph{sqrt(2x+6)+1 [-10, 10, -5, 5]}

Graph-3