To find the minimum point of the function $s(x) = \sqrt{x + 4}$, let’s analyze it step-by-step.

1. Domain Analysis: The square root function $\sqrt{x + 4}$ is defined when $x + 4 \geq 0$, or $x \geq -4$.

2. Behavior of the Function: Since square root functions are generally increasing, $s(x) = \sqrt{x + 4}$ will increase as $x$ increases within its domain $x \geq -4$.

3. Finding the Minimum Point:

   • The smallest value $x$ can take is $x = -4$.
   • Substituting $x = -4$ into $s(x)$: $s(-4) = \sqrt{-4 + 4} = \sqrt{0} = 0$

   So, the minimum point is at $(-4, 0)$.

4. Conclusion: The correct answer is C. $(-4, 0)$.

Would you like more details or have any questions about the steps?

Related Questions

1. What is the domain and range of $s(x) = \sqrt{x + 4}$?
2. How do you determine whether a square root function is increasing or decreasing?
3. How do you find the minimum of a function that involves a square root?
4. What is the general shape of a square root function on a graph?
5. How would the minimum point change if we modified $s(x) = \sqrt{x + 4}$ to $s(x) = \sqrt{x - 4}$?

Tip: For functions involving square roots, analyzing the domain is crucial to understanding where the function is defined and where it might reach its minimum or maximum values.