How does the graph of \( y=\sqrt{x} \) change when the function is changes to \( y=\frac{1}{2} \sqrt{x} \) ? (1 point) The graph is shifted \( \frac{1}{2} \) units up on the \( x \)-axis The graph is shifted \( \frac{1}{2} \) units up on the \( y \)-axis The graph is vertically compressed by a factor of \( \frac{1}{2} \) The graph is vertically stretched by a factor of \( \frac{1}{2} \)

When the function is changed from \( y=\sqrt{x} \) to \( y=\frac{1}{2} \sqrt{x} \), the key change is that the graph undergoes a vertical compression by a factor of \( \frac{1}{2} \). This means every point on the original graph of \( y=\sqrt{x} \) is pulled closer to the x-axis, making the curve flatter. To visualize this, imagine the original graph stretching up like a tall building. Now, if you take a little off the top, the building becomes shorter, but it still stands on the same foundation. So, while the x-values remain unaffected, the heights (y-values) of points on the graph are halved, emphasizing the compression without shifting the graph up or down.