1. **State the problem:** Match each given equation with the corresponding colored graph based on the description and the shape of the graphs. 2. **Recall the base function:** The base function is $y=\sqrt{x}$, which starts at the origin $(0,0)$ and increases to the right. 3. **Analyze each equation:** - $y=2\sqrt{x}$: This is a vertical stretch of $y=\sqrt{x}$ by a factor of 2, so it lies above the black curve. - $y=0.5\sqrt{x}$: This is a vertical compression by a factor of 0.5, so it lies below the black curve but above the x-axis. - $y=\sqrt{-x}$: This reflects the graph of $y=\sqrt{x}$ across the y-axis, so it extends leftwards. - $y=-\sqrt{x}$: This reflects the graph of $y=\sqrt{x}$ across the x-axis, so it lies below the x-axis. 4. **Match with colors based on the description:** - Green curve (G): below and close to black curve $\Rightarrow y=0.5\sqrt{x}$ - Orange curve (O): above black curve $\Rightarrow y=2\sqrt{x}$ - Red curve (R): leftwards reflection $\Rightarrow y=\sqrt{-x}$ - Blue curve (B): below x-axis $\Rightarrow y=-\sqrt{x}$ 5. **Final matching:** - a. green $\to y=0.5\sqrt{x}$ - b. orange $\to y=2\sqrt{x}$ - c. red $\to y=\sqrt{-x}$ - d. blue $\to y=-\sqrt{x}$