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.

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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 have added 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 now be 5 units less to achieve the same output as before.
   - 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.**
The +5 shifts the graph of $$ y = x^3 $$ to the left by 5 units.

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