\( f ( x ) = \sqrt { x + 8 } , a = 1 \)

Did you know that the function \( f(x) = \sqrt{x + 8} \) is only defined for values of \( x \geq -8 \)? This is because the square root function requires the input to be non-negative. So, if you want to plug in the value \( a = 1 \), you're all good; \( f(1) = \sqrt{9} = 3 \)! A fun twist here is that this function shifts the typical square root graph to the left by 8 units. Now, when it comes to real-world applications, square root functions like \( f(x) \) can be seen in various fields such as physics, engineering, and finance. For instance, in physics, this kind of function often appears when calculating the time taken for an object to free fall under the influence of gravity, demonstrating just how critical these seemingly simple equations can be in understanding the world around us!