Let us analyze and solve the given graphs based on the parent function $f(x) = x^3$.

Graph (a):

From the graph, the shape resembles the cubic parent function $y = x^3$, but it has been shifted vertically upwards by 2 units. There is no horizontal shift or scaling.

Thus, the equation for (a) is: $y = x^3 + 2$

Graph (b):

The graph appears to be a reflection of the parent function $y = x^3$ across the x-axis (negative cubic). Additionally, it has been horizontally shifted 2 units to the right. This means the transformation involves negation and horizontal translation.

Thus, the equation for (b) is: $y = -(x - 2)^3$

Final Answers:

1. (a): $y = x^3 + 2$
2. (b): $y = -(x - 2)^3$

Do you need further explanations or a detailed breakdown? Let me know!

Here are 5 questions related to the transformations of functions:

1. What would the graph look like if we shifted $y = x^3$ down by 4 units?
2. How does the graph of $y = -x^3$ compare to $y = x^3$?
3. What happens to the graph of $y = x^3$ when it is horizontally shifted left by 3 units?
4. How do vertical stretches or compressions affect the graph of $y = x^3$?
5. What transformations would result in the equation $y = (x + 1)^3 - 5$?

Tip: Always observe changes in the graph's shape (reflection or stretch) and the movement (shift) to determine the transformations step by step!