Questions: y=3 sqrt(x) Domain: All real numbers. Range: All real numbers. Domain: x ≥ 0 Range: y ≥ 0 Domain: x ≤ 0 Range: y ≥ 0 Domain: x ≥ -1 Range: y ≥ 2

Solution Steps

To determine the correct domain and range for the function \( y = 3 \sqrt{x} \), we need to consider the properties of the square root function. The square root function is only defined for non-negative values of \( x \), which means the domain is \( x \geq 0 \). The range of the function is determined by the output values of \( y \), which are also non-negative since the square root of a non-negative number is non-negative. Therefore, the range is \( y \geq 0 \).

The function given is \( y = 3 \sqrt{x} \). The square root function, \( \sqrt{x} \), is only defined for non-negative values of \( x \). Therefore, the domain of the function is \( x \geq 0 \).

For the function \( y = 3 \sqrt{x} \), as \( x \) takes on values from the domain \( x \geq 0 \), the output \( y \) will also be non-negative. This is because the square root of a non-negative number is non-negative, and multiplying by 3 does not change the sign. Therefore, the range of the function is \( y \geq 0 \).

Given the options:

• A) Domain: \{ All real numbers. \} Range: \{ All real numbers. \}
• B) Domain: \( x \geq 0 \) Range: \( y \geq 0 \)
• C) Domain: \( x \leq 0 \) Range: \( y \geq 0 \)
• D) Domain: \( x \geq -1 \) Range: \( y \geq 2 \)

The correct answer is B, as it matches the determined domain and range.

Final Answer