Asked by Sigma

Which graph accurately demonstrates the relationship between the functions f(x)=x−−√
and f(x)=x−−√+3 ?


A. The first curve is solid and begins at coordinates left parenthesis 0 comma 3 right parenthesis. The first curve passes through approximate coordinates left parenthesis 1 comma 4 right parenthesis, left parenthesis 2 comma 4.5 right parenthesis, and left parenthesis 3 comma 4.8 right parenthesis. The second curve is dotted and begins at coordinates left parenthesis 0 comma negative 3 right parenthesis. The second curve passes through approximate coordinates left parenthesis 1 comma negative 2 right parenthesis, left parenthesis 2 comma negative 1.5 right parenthesis, and left parenthesis 3 comma negative 1.2 right parenthesis.
B. The first curve is solid and begins at coordinates left parenthesis 0 comma 1 right parenthesis. The first curve passes through approximate coordinates left parenthesis 1 comma 2 right parenthesis, left parenthesis 2 comma 2.5 right parenthesis, and left parenthesis 3 comma 2.8 right parenthesis. The second curve is dotted and begins at coordinates left parenthesis 0 comma negative 2 right parenthesis. The second curve passes through approximate coordinates left parenthesis 1 comma negative 1 right parenthesis, left parenthesis 2 comma negative 0.5 right parenthesis, and left parenthesis 3 comma negative 0.2 right parenthesis.
C. The first curve is solid and begins at coordinates left parenthesis 0 comma 0 right parenthesis. The first curve passes through approximate coordinates left parenthesis 1 comma 1 right parenthesis, left parenthesis 2 comma 1.5 right parenthesis, and left parenthesis 3 comma 1.8 right parenthesis. The second curve is dotted and begins at coordinates left parenthesis 0 comma negative 3 right parenthesis. The second curve passes through approximate coordinates left parenthesis 1 comma negative 2 right parenthesis, left parenthesis 2 comma negative 1.5 right parenthesis, and left parenthesis 3 comma negative 1.2 right parenthesis.
D. The first curve is solid and begins at coordinates left parenthesis 0 comma 0 right parenthesis. The first curve passes through approximate coordinates left parenthesis 1 comma 1 right parenthesis, left parenthesis 2 comma 1.5 right parenthesis, and left parenthesis 3 comma 1.8 right parenthesis. The second curve is dotted and begins at coordinates left parenthesis 0 comma 3 right parenthesis. The second curve passes through approximate coordinates left parenthesis 1 comma 4 right parenthesis, left parenthesis 2 comma 4.5 right parenthesis, and left parenthesis 3 comma 4.8 right parenthesis.

All Answers 1

Answered by GPT-5 mini AI
D

Reason: √x has starting point (0,0) and values (1,1), (2≈1.5), (3≈1.8). Adding 3 shifts the graph up by 3, so √x+3 starts at (0,3) and has (1,4), (2≈4.5), (3≈4.8), which matches option D.