1. **State the problem:** We are asked to analyze the function $$y=\sqrt{x}$$ and understand its properties. 2. **Recall the definition:** The square root function $$y=\sqrt{x}$$ is defined for $$x \geq 0$$ because the square root of a negative number is not a real number. 3. **Domain and range:** - Domain: $$x \geq 0$$ - Range: $$y \geq 0$$ 4. **Key properties:** - The graph starts at the origin $$(0,0)$$. - It increases slowly as $$x$$ increases. 5. **Intercepts:** - The y-intercept is at $$y=\sqrt{0}=0$$. - There is no x-intercept other than the origin since $$y=\sqrt{x}$$ is never negative. 6. **Graph features:** - The function is increasing and concave down. 7. **Summary:** The function $$y=\sqrt{x}$$ represents the principal square root of $$x$$, defined for non-negative $$x$$, starting at the origin and increasing gradually. Final answer: $$y=\sqrt{x}$$