Question

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

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
Image with description 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.

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
Image with description 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.

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
Image with description 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.

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
Image with description 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.

Answer 1

The correct graph is the one where both curves begin at x = 0 (domain x ≥ 0), have the same shape, and one is exactly 3 units above the other — i.e. they start at (0,0) and (0,3). This shows f(x)=√x and f(x)=√x+3 (the second is the first shifted up by 3).