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Let's break down the problem and answer the questions step by step.

### Function: 
The given function is:
\[ g(x) = x^2 - 6 \]

### a) **Choose the correct parent function.**
The parent function refers to the basic function before any transformations are applied.

- The parent function here is \( y = x^2 \), because the given function is a quadratic function with a vertical shift.
- **Answer**: \( y = x^2 \)

### b) **Choose the correct transformation (Reflections).**
There is no reflection in this case. The function does not have a negative coefficient in front of the \( x^2 \) term, which would indicate a reflection over the x-axis.
- **Answer**: No reflection.

### c) **Choose the correct transformation (Stretches/Compressions).**
There are no stretches or compressions because the coefficient of \( x^2 \) is 1, which means no vertical or horizontal scaling is applied.
- **Answer**: No stretches or compressions.

### d) **Choose the correct transformation (Vertical Shifts).**
The term \( -6 \) indicates a vertical shift of 6 units down.
- **Answer**: Vertical shift down by 6 units.

### e) **Choose the correct transformation (Horizontal Shifts).**
There are no horizontal shifts because the function has no terms that affect the \( x \)-coordinate (e.g., nothing like \( (x - h)^2 \)).
- **Answer**: No horizontal shift.

Let me know if you'd like further clarification or explanations on these transformations!

### Expanding on these concepts, here are some related questions:
1. How would a reflection over the x-axis affect the equation of the function?
2. What would happen to the graph if the \( -6 \) was instead added to the \( x \)-term?
3. How would the graph of \( g(x) = 2x^2 - 6 \) compare to the original function?
4. How do horizontal shifts affect the function's vertex in quadratic functions?
5. What is the vertex form of a quadratic equation and how does it help in identifying transformations?

### Tip:
When analyzing transformations of functions, always check for changes in the coefficients of \( x \), constants outside of the function, and any modifications within the parentheses to determine shifts, reflections, and stretches/compressions.

Determine the parent function from which the graph of the function g(x) = x^2 - 6 can be obtained. Identify each transformation that can be applied to the parent function in order to obtain the graph of the function.

Understand how to determine the parent function and apply transformations such as vertical shifts to obtain the graph of the function g(x) = x^2 - 6. This problem covers quadratic functions and the effects of various transformations.

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