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The given function transformation is \( g(x) = -3f(x - 1) + 1 \), where \( f(x) = x \) is the parent function.

To graph the transformation:

1. **Horizontal Shift**: The term \( (x - 1) \) indicates a shift **1 unit to the right**.
2. **Vertical Stretch/Reflection**: The coefficient \( -3 \) means the graph is vertically stretched by a factor of 3 and reflected over the x-axis.
3. **Vertical Shift**: The \( +1 \) moves the entire graph **1 unit up**.

### Step-by-step breakdown:
- Start by shifting the line \( f(x) = x \) 1 unit to the right.
- Then apply the vertical stretch and reflection by multiplying the slope by -3 (i.e., slope becomes -3).
- Finally, move the graph up by 1 unit.

Would you like a detailed step-by-step plotting of the points, or have any specific questions?

### 5 Related Questions:
1. What effect does a negative coefficient have on a function's graph?
2. How does a horizontal shift affect the domain of a function?
3. What is the difference between a vertical stretch and compression?
4. Can you explain how transformations apply to non-linear functions like quadratics?
5. How do combined transformations (like shift and reflection) affect the overall graph?

### Tip:
Remember, transformations like stretches and shifts can be applied in sequence, but order matters—typically, handle horizontal transformations before vertical ones!

Given the linear parent function f(x) = x, graph the transformation g(x) = -3f(x - 1) + 1.

Learn how to graph the transformation g(x) = -3f(x - 1) + 1 from the parent function f(x) = x. This problem involves horizontal shifting, vertical stretching, and reflection over the x-axis. Suitable for students in Grades 9-11.

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