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 \( f(x) = (x + 5)^{3} \) showcases a shift of the graph of the original function \( y = x^{3} \). When we add 5 inside the parentheses with \( x \), this causes the entire graph to move to the left by 5 units. So the correct description is that the +5 affects the \( x \)-values, resulting in a horizontal shift of the graph. Understanding this concept is crucial for graphing transformations! Often, students mistakenly think that adding a constant inside the function shifts the graph vertically, when in fact it’s the opposite. Drawing a few graphs and experimenting with different values can clarify these transformations quite easily.