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The question shown in the image asks to graph the function \( g(x) = \sqrt[3]{x} - 5 \) using transformations of the cube root function \( f(x) = \sqrt[3]{x} \). Let's go through the steps needed to analyze and select the correct graph.

### Function Breakdown:
- The base function is \( f(x) = \sqrt[3]{x} \), which is the cube root function.
- The transformation involved is a **vertical translation** downward by 5 units. This is due to the "-5" outside the cube root, meaning the entire graph of \( f(x) \) is shifted down.

### Steps to graph:
1. **Base Function:** Start with the graph of \( f(x) = \sqrt[3]{x} \). This function passes through the origin (0,0), and its general shape is an increasing curve.
2. **Vertical Shift:** Subtracting 5 from \( f(x) \) shifts every point on the graph of \( \sqrt[3]{x} \) downward by 5 units. So, instead of passing through (0,0), the graph now passes through (0, -5).

### Now, check the graphs in the provided options:
- We are looking for the cube root graph, which has been shifted down by 5 units.
  
From the options:
- **Option A:** Shows a curve with the right behavior, starting at (0, -5).
- The other options (B, C, D) either do not shift downwards correctly or have a different behavior.

Thus, **Option A** is the correct graph.

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Would you like any further details about graphing transformations?

### 5 Related Questions:
1. How do horizontal translations affect the graph of a function?
2. What is the difference between vertical and horizontal shifts in graphing?
3. How does scaling (stretching or compressing) affect the graph of a cube root function?
4. How do you find the domain and range of cube root functions?
5. How would adding a coefficient to \( \sqrt[3]{x} \) affect the graph?

### Tip:
When graphing transformations, always start by analyzing the base function's key points and behavior before applying shifts or stretches!

Use transformations of the cube root function, f(x) = ³√x, to graph the function g(x) = ³√x - 5. Choose the correct graph below.

Learn how to graph the function g(x) = ³√x - 5 using transformations of the cube root function. This problem demonstrates a vertical translation and is ideal for students in Grades 9-11.

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