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)
Option #
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Answer 1

To determine which function matches the described graph in the first quadrant, we can analyze the given options:

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

   • The term \( 2\sqrt{x} \) indicates that this function will start at \( f(0) = 2\sqrt{0} - 3 = -3 \) and increase as \( x \) increases, but it starts negative and does not intersect the x-axis until it exceeds a certain value of \( x \).

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

   • The term \( 2\sqrt{x} \) indicates that this function will start at \( f(0) = 2\sqrt{0} = 0 \) and will increase positively as \( x \) increases. This means it will be in the first quadrant and will not be negative.

Since the question specifies that the solid curve is plotted in the first quadrant, the graph must intersect the y-axis at or above zero and also maintain positive values as \( x \) increases.

Based on this analysis, Option #2 \( f(x) = 2\sqrt{x} \) matches the graph as it remains in the first quadrant.

Therefore, the answer is:

Option #2.