Question

Use the image to answer the 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

Based on the equations given in the options, we need to analyze each function:

1. **Option #1: \( f(x) = 2\sqrt{x} - 3 \)**
- This function represents a transformed square root function. The base function \( y = \sqrt{x} \) typically starts at (0,0) and increases as \( x \) increases. Multiplying by 2 stretches it vertically, and subtracting 3 shifts the graph down by 3 units. Therefore, for values of \( x \) greater than or equal to 0, the graph starts at -3 and moves upwards.

2. **Option #2: \( f(x) = 2\sqrt{x} \)**
- This option also represents a square root function but without any vertical shifts. It starts at (0,0) and increases positively as \( x \) increases. This function will stay in the first quadrant for non-negative values.

Given that the curve passes through the first quadrant, which indicates positive values for both \( x \) and \( f(x) \), it seems likely that the function that could match this graph would be the one without a downward shift.

Therefore, **Option #2** is more likely to correspond to the graph described, since \( f(x) = 2\sqrt{x} \) remains in the first quadrant for \( x \geq 0 \).

If you already have a visual reference, check if the curve starts from (0,0) and moves upward in the first quadrant. If it does, then choose **Option #2**. If it starts lower and shifts down, then choose **Option #1**. However, typically for a standard positive curve in the first quadrant, **Option #2** is likely to be the matching graph.