Final answer:
The graph of g(x) = -2f(x), where f(x) = √x, is a vertically stretched and reflected version of the square root parent function, opening downwards, only for non-negative x values.a
Step-by-step explanation:
The parent function mentioned is f(x) = √x, which represents the square root function. When we apply the transformation g(x) = -2f(x), we are essentially stretching the graph by a factor of 2 and reflecting it across the x-axis because of the negative sign. To visualize this, each point on the graph of the original function will be multiplied by -2 in the y-direction, which makes the resulting graph open downwards rather than upwards. Since the square root function only contains non-negative x values (because the square root of a negative number is not a real number), the graph of g(x) will also be restricted to the right side of the y-axis. The graph will look like a mirror image of the parent function across the x-axis, stretched vertically by a factor of 2.