Range Square Root 356A61

1. **State the problem:** We need to find the range of the function $$y = \sqrt{x}$$. 2. **Recall the domain and range of the square root function:** The square root function $$\sqrt{x}$$ is defined only for $$x \geq 0$$ because the square root of a negative number is not a real number. 3. **Determine the output values (range):** Since $$y = \sqrt{x}$$, as $$x$$ increases from $$0$$ to infinity, $$y$$ takes values starting from $$0$$ and increases without bound. 4. **Check the possible values of $$y$$:** - When $$x = 0$$, $$y = \sqrt{0} = 0$$. - When $$x > 0$$, $$y = \sqrt{x} > 0$$. 5. **Conclusion:** The range of $$y = \sqrt{x}$$ is all real numbers $$y$$ such that $$y \geq 0$$. **Final answer:** $$\{ y \mid y \geq 0 \}$$