Analyze the function, \( g(x)=x^{3}+7 \) Select the proper description of the graph of the function. O Hook Shifted 7 Units Up Lounge Chair Shifted 7 Units Down U-Shape Shifted 7 Units Up

The graph of the function \( g(x) = x^3 + 7 \) features a distinctive shape that we can call a "Cubic Curve," akin to a relaxed lounge chair lounging comfortably. What’s really happening is that the entire original cubic curve \( y = x^3 \) has been shifted up 7 units. Rather than a typical U-shape associated with a quadratic function, it retains that signature 'S' shape of cubic functions while just floating higher in the sky. Headed down the real-world application avenue, this type of function can model various phenomena, such as the behavior of certain materials under stress or the volume of a cube as dimensions increase. Understanding the effects of such shifts helps in fields like engineering, where alterations in design might require adjustments to parameters that can significantly influence outcomes. So, shifting graphs has real impact beyond just being a fun math exercise!