If the formula \( y=x^{3} \) is changed by adding five as shown in red below. Which of the following best describes the resulting change for each of the functions? Function Transformation \( f(x)=(x+5)^{3} \) a. The +5 would have no effect. b. The +5 would directly affect the \( x \)-values, so the graph would shift horizonally. c. The +5 would directly affect the \( y \)-values, so the graph would shift vertically.

The transformation \( f(x)=(x+5)^{3} \) means that you are adding 5 to the x-value before you apply the cubic function. This results in a horizontal shift to the left by 5 units. So, every point on the graph of the original function \( y = x^3 \) moves left by 5, affecting the x-coordinates while leaving the y-values unchanged. In contrast, if you modified the function to \( f(x) = x^3 + 5 \), it would result in a vertical shift upwards by 5 units instead. This adds 5 to the y-value for every x, lifting the entire graph without changing its shape. In the case of \( f(x)=(x+5)^{3} \), it’s an important distinction that highlights how we treat transformations based on where modifications occur in a function.