Determine which graph matches the function f(x)=3x−−√

Question

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Option #1:

A coordinate plane's axes range from negative 4 to 4, both by 1-unit increments. An S-shaped curve is plotted passing through the first and third quadrants.



Option #2:

A coordinate plane's x-axis ranges from negative 2 to 4 and its y-axis ranges from negative 2 to 6, both by 1-unit increments. A curve is plotted in quadrant 1.

(1 point)
Option #

Answer 1

To determine which graph matches the function \( f(x) = \sqrt{3x} \), we need to analyze the characteristics of the function.

1. The function \( f(x) = \sqrt{3x} \) is defined only for \( x \geq 0 \) (since the square root of a negative number is not defined in the context of real numbers).
2. As \( x \) increases, \( f(x) \) also increases, starting from \( f(0) = 0 \).
3. The function will pass through points such as \( (0, 0) \), \( (1, \sqrt{3}) \), \( (4, 6) \), etc., indicating that it remains in the first quadrant after \( x = 0 \).

Now evaluating the options:

• Option #1: The description mentions an S-shaped curve passing through the first and third quadrants. However, since \( f(x) = \sqrt{3x} \) does not exist in the third quadrant, this cannot be the correct option.

• Option #2: The description states that a curve is plotted in quadrant 1 and is defined for \( x \geq 0 \). This fits the behavior of \( f(x) = \sqrt{3x} \), which exists only in the first quadrant and increases as \( x \) increases.

Therefore, Option #2 is the one that matches the function \( f(x) = \sqrt{3x} \).