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 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.

When you add +5 to the function \( y = x^{3} \) to create \( y = x^{3} + 5 \), this transformation shifts the entire graph upward by 5 units. This means that for every x-value, the output of the function increases by 5, directly affecting the y-values. So, if you're looking at point (1,1) on the original graph, this point would move to (1,6) on the transformed graph, reflecting how each point rises vertically without moving left or right. Thus, the correct choice is c: The +5 would directly affect the \( y \)-values, so the graph would shift vertically. When interpreting transformations, it's helpful to visualize how functions behave with changes. Adding a number outside the function always affects the graph vertically, while adding it inside (like \( y = (x + 5)^{3} \)) would shift the graph horizontally. Keep this trick in mind, and you'll ace transformations in no time!