Question

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

Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.
▼Click for Long Desc
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.

Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 6 to 6 in increments of 2.
▼Click for Long Desc
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.

Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 2.
▼Click for Long Desc
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.

Two curves are graphed on a coordinate plane. The x-axis ranges from negative 3 to 3 in increments of 1. The y-axis ranges from negative 4 to 4 in increments of 2.
▼Click for Long Desc
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.

Answer 1

The second graph.

Reason: f(x)=√x starts at (0,0) and goes through (1,1),(2,≈1.41),(3,≈1.73). f(x)=√x+3 is that same curve shifted up 3, so it starts at (0,3) and goes through (1,4),(2,≈4.41),(3,≈4.73), matching the second option.