If the formula \( y=x^{3} \) is changed by adding five as shown in red below. \( f(x)=(x+5)^{3} \) Which values would be most directly affected by the change?

This change shifts the graph of the function horizontally. Specifically, the transformation \( f(x)=(x+5)^{3} \) moves the graph of \( y=x^{3} \) five units to the left. This means that all x-values that yield the same y-value are affected, and the point that was originally at \( (0,0) \) in \( y=x^{3} \) will now be located at \( (-5,0) \) in \( f(x) \). Essentially, key characteristics like intercepts and turning points shift with this transformation. When examining the function, it’s important to remember that while x-values have adjusted, the shape of the graph remains cubic. The transformation affects where the function intersects the x-axis and its symmetry but will not alter the ultimate behavior of the cubic function, which still approaches infinity in both the positive and negative directions as x moves away from zero.