Which transformations have been performed on the graph of \( f(x)=\sqrt{x} \) to obtain the graph of \( g(x)=-0.3 \sqrt{x}-4 \) ? Select each correct answer. Select 3 correct answer(s) reflect the graph over the x-axis stretch the graph away from the x-axis compress the graph closer to the x-axis translate the graph to the right translate the graph to the left translate the graph down

To obtain the graph of \( g(x) = -0.3 \sqrt{x} - 4 \) from \( f(x) = \sqrt{x} \), there are several transformations at play. First, the negative sign in front of the \( 0.3 \) indicates that the graph is reflected over the x-axis. This means all y-values are inverted, transforming the shape of the graph below the x-axis. Next, the \( -4 \) term represents a vertical translation down by 4 units. This moves the entire graph downward, adjusting all y-values down by 4. Finally, the coefficient \( -0.3 \) acts as a vertical compression towards the x-axis. This changes the steepness of the graph, making it closer to the x-axis than the original function typically would be. So the three correct transformations are: reflect the graph over the x-axis, translate the graph down, and compress the graph closer to the x-axis.