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.

To analyze the transformation of the function \( y = x^3 \) when it is changed to \( f(x) = (x + 5)^3 \), we need to understand how the addition of 5 affects the function. 1. **Original Function**: The original function is \( y = x^3 \). This is a cubic function that passes through the origin (0,0) and has a specific shape. 2. **Transformed Function**: The transformed function is \( f(x) = (x + 5)^3 \). Here, we are adding 5 inside the parentheses with \( x \). 3. **Effect of the Transformation**: - When we add a constant inside the function (in this case, \( +5 \) with \( x \)), it affects the \( x \)-values directly. Specifically, it shifts the graph to the left by 5 units. This is because for any given \( y \)-value, the \( x \)-value must be 5 less than it was in the original function to achieve the same output. - Therefore, the graph of \( f(x) = (x + 5)^3 \) will be the same shape as \( y = x^3 \) but shifted horizontally to the left. Based on this analysis, the correct answer is: **b. The +5 would directly affect the \( x \)-values, so the graph would shift horizontally.**