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

Transcript text: $y=3 \sqrt{x}$ Domain: \{ All real numbers. \} Range: $\{$ All real numbers. \} Domain: $x \geq 0$ Range: $y \geq 0$ Domain: $x \leq 0$ Range: $y \geq 0$ Domain: $x \geq-1$ Range: $y \geq 2$

Solution

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 $.

Step 1: Determine the Domain of the Function

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 $.

Step 2: Determine the Range of the Function

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 $.

Step 3: Identify the Correct Multiple-Choice Answer

Given the options: