Describe how the function \( f(x)=-4 \sqrt{x}+2 \) is a transformation of a toolkit function. This is a square root function stretched vertically by a factor of 4 , reflected vertically across the \( x \)-axis, and then shifted up 2 units. This is a square root function stretched horizontally by a factor of 4 , reflected vertically across the \( x \)-axis, and then shifted up 2 units. This is a square root function stretched vertically by a factor of 4 , reflected horizontally across the \( x \)-axis, and then shifted up 2 units. This is a square root function compressed vertically by a factor of 4 , reflected vertically across the \( x \)-axis, and then shifted up 2 units.

The function \( f(x) = -4 \sqrt{x} + 2 \) can be understood as a transformation of the basic square root function \( \sqrt{x} \). Here's a step-by-step breakdown of the transformations applied: 1. **Vertical Stretch by a Factor of 4**: The coefficient **-4** in front of the square root indicates that the graph is stretched vertically by a factor of 4. This means that for each \( x \), the \( y \)-values are multiplied by 4, making the graph four times taller than the original square root function. 2. **Reflection Across the \( x \)-Axis**: The negative sign **(-)** before the 4 means that the graph is also reflected vertically across the \( x \)-axis. This flips the graph upside down. 3. **Vertical Shift Upwards by 2 Units**: The constant **+2** at the end signifies that the entire graph is shifted upwards by 2 units. This moves the graph higher along the \( y \)-axis. Putting it all together, the function \( f(x) = -4 \sqrt{x} + 2 \) represents a square root function that is **stretched vertically by a factor of 4**, **reflected vertically across the \( x \)-axis**, and then **shifted up 2 units**. **Correct Description:** *This is a square root function stretched vertically by a factor of 4, reflected vertically across the \( x \)-axis, and then shifted up 2 units.*