Question

Which statement best describes the relationship between the functions f(x)=x−−√
and f(x)=x−−√−3
?(1 point)
Responses

f(x)=x−−√−3
is the same as f(x)=x−−√
translated down 3 units.
f left parenthesis x right parenthesis equals Start Root x End Root minus 3 is the same as f left parenthesis x right parenthesis equals Start Root x End Root translated down 3 units.

f(x)=x−−√−3
is the same as f(x)=x−−√
translated up 3 units.
f left parenthesis x right parenthesis equals Start Root x End Root minus 3 is the same as f left parenthesis x right parenthesis equals Start Root x End Root translated up 3 units.

f(x)=x−−√−3
is the same as f(x)=x−−√
translated to the left 3 units.
f left parenthesis x right parenthesis equals Start Root x End Root minus 3 is the same as f left parenthesis x right parenthesis equals Start Root x End Root translated to the left 3 units.

f(x)=x−−√−3
is the same as f(x)=x−−√
translated to the right 3 units.

Answer 1

"f(x)=√x − 3 is the same as f(x)=√x translated down 3 units."

Reason: subtracting 3 moves every y-value down 3 (vertical translation), changing the range from [0,∞) to [-3,∞) but leaving the domain [0,∞) unchanged.