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

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Answer 1 · 2017-01-13T14:37:44

See 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