Use the image to answer the question.

Question

A coordinate plane's axes range from negative 2 to 4, both by 1-unit increments. A solid curve is plotted passing through the first quadrant.

Select the option that matches the graph.

Option #1: The graph of the function matches f(x)=2x−−√3
.

Option #2: The graph of the function matches f(x)=2x−−√
.

(1 point)

Answer 1

To determine which option matches the graph described, we need to analyze the functions given in both options.

1. Option #1: \( f(x) = 2\sqrt{x} - 3 \)

   • This function starts at \( f(0) = 2\sqrt{0} - 3 = -3 \) and increases as \( x \) increases. Since it involves the square root, it will only be defined for \( x \geq 0 \), leading to a curve that starts below the x-axis and rises towards the right.

2. Option #2: \( f(x) = 2\sqrt{x} \)

   • This function starts at \( f(0) = 2\sqrt{0} = 0 \) and increases for \( x \geq 0 \) but does not dip below the x-axis. This means the entire graph is located in the first quadrant.

Given that you mentioned the curve passes through the first quadrant, this suggests that Option #2, \( f(x) = 2\sqrt{x} \), will effectively match the description provided in the question.

So the correct answer would be Option #2: The graph of the function matches \( f(x) = 2\sqrt{x} \).