1. **State the problem:** We are given the function $f(x) = \sqrt{x-4}$ and asked to understand its domain, range, and graph. 2. **Domain:** The expression inside the square root must be non-negative for real values, so: $$x - 4 \geq 0$$ $$x \geq 4$$ Thus, the domain is $[4, \infty)$. 3. **Range:** Since the square root function outputs values greater than or equal to zero, and the smallest value inside the root is zero (when $x=4$), the range is: $$[0, \infty)$$ 4. **Graph description:** The graph starts at the point $(4,0)$ because $f(4) = \sqrt{4-4} = 0$. 5. For $x > 4$, $f(x)$ increases as the square root of $(x-4)$, so the graph extends rightwards and upwards. 6. The function is a horizontal shift of the basic square root function $y=\sqrt{x}$ by 4 units to the right. **Final answer:** - Domain: $[4, \infty)$ - Range: $[0, \infty)$ - Graph starts at $(4,0)$ and increases rightwards.