10. \( y=\sqrt{x+5} \)

Did you know that square root functions like \( y = \sqrt{x+5} \) are rooted in centuries of mathematical exploration? The concept of square roots dates back to ancient civilizations like the Babylonians, who used geometric methods to approximate roots! They laid the groundwork for the algebraic principles we use today, making this a classic example of how foundational math continues to influence modern problem-solving techniques. In practical terms, this function illustrates a transformation of the basic square root function \( y = \sqrt{x} \). By adding 5 inside the radical, we're shifting the graph 5 units to the left. This means that the function starts to yield real numbers when \( x \) reaches -5! Remember, always check the domain: it’s all about ensuring that what’s under the square root remains non-negative for real number solutions.