which of the following is the graph of $y = - 4sqrt{x}$?

Answer:

The correct graph is the one that starts at the origin (0,0) and curves downward in the right half-plane (x ≥ 0).

Explanation:

Step 1: Determine the domain

The function ( y = -4\sqrt{x} ) requires ( x \geq 0 ), so the graph exists only for non-negative x-values.

Step 2: Analyze the parent function transformation

The parent function is ( y = \sqrt{x} ), which curves upward from the origin. The negative sign reflects it over the x-axis, and the coefficient 4 vertically stretches it by a factor of 4, making it curve downward more steeply.

Step 3: Evaluate key points

At ( x = 0 ), ( y = 0 ). At ( x = 1 ), ( y = -4 ). At ( x = 4 ), ( y = -8 ). The graph should pass through these points, curving downward as x increases.