https://file.aiquickdraw.com/mathbot/file/1726685856463cgp5wg4t.jpg

Let's go through this step-by-step to solve the given problem.

### Given Function:
\[ f(x) = \sqrt[3]{x} - 3 \]

#### Part a: Parent Function
The function involves a cube root, so the parent function is:
\[
y = \sqrt[3]{x}
\]

Thus, the correct parent function is:
- \( y = \sqrt[3]{x} \)

#### Part b: Reflections
There is no negative sign in front of the cube root, so there is **no reflection**.

#### Part c: Stretches/Compressions
The function does not have a coefficient multiplying \( \sqrt[3]{x} \), so there is **no vertical stretch or compression**.

#### Part d: Vertical Shifts
The function has \( -3 \) added outside the cube root, which represents a **vertical shift down by 3 units**.

#### Part e: Horizontal Shifts
There is no transformation inside the cube root (i.e., no term added or subtracted from \( x \)), so there is **no horizontal shift**.

### Summary:
1. **Parent function:** \( y = \sqrt[3]{x} \)
2. **Reflections:** None.
3. **Stretches/Compressions:** None.
4. **Vertical Shifts:** Down 3 units.
5. **Horizontal Shifts:** None.

Let me know if you'd like further details or have any questions. 

Here are some related questions for practice:
1. What would the transformation be if the function was \( f(x) = -\sqrt[3]{x} - 3 \)?
2. How would a horizontal shift affect the function \( f(x) = \sqrt[3]{x} - 3 \)?
3. What is the difference between vertical and horizontal shifts?
4. How would a coefficient in front of \( \sqrt[3]{x} \) affect the graph?
5. Can a cubic root function have a reflection and a vertical shift simultaneously?

**Tip:** Always check for transformations both inside and outside the root or any function to understand its graph!

Determine the parent function from which the graph of the function shown below can be obtained. Next, identify each transformation that can be applied to the parent function in order to obtain the graph of the function shown below. f(x) = ∛x - 3.

Explore how to find the parent function of the cube root function f(x) = ∛x - 3 and identify the transformations involved, such as vertical shifts and reflections. This detailed step-by-step guide is perfect for students in Grades 9-12.

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