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

Answer 1

Ariana Alvarez

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

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Answer 2

Anna Allen

To obtain the graph ( y = \sqrt{2(x + 3)} + 1 ) from ( y = \sqrt{x} ), you need to apply the following transformations:

Horizontal translation left by 3 units due to ( (x + 3) ).
Vertical stretch by a factor of 2 due to ( \sqrt{2} ).
Vertical translation up by 1 unit due to ( +1 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.