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 function \( f(x) = (x + 5)^{3} \) indicates a horizontal transformation. When you replace \( x \) with \( x + 5 \), it shifts the entire graph of the function to the left by 5 units. So, the original function \( y = x^{3} \) will move left, making the behavior and values of the function change accordingly. As for the real-world application, horizontal shifts are common when modeling real-life situations, like adjusting time scales or geographical positions. For example, if \( x \) represents time in hours, an additional 5 hours can reflect a change in start time, affecting how we view data progression in scenarios like project timelines or event planning.