Given the function \( g(x) = f(-x) - 1 \), this expression indicates that \( g(x) \) is derived from the function \( f(x) \) by applying two transformations:

1. **Horizontal reflection**: Replacing \( x \) with \( -x \) reflects the graph of \( f(x) \) across the y-axis. This means that for each point \( (x, f(x)) \) on the graph of \( f(x) \), there is a corresponding point \( (-x, f(-x)) \) on the graph of \( g(x) \).
   
2. **Vertical shift**: Subtracting 1 from \( f(-x) \) moves the entire graph down by 1 unit. This transformation affects all the y-values by decreasing them by 1.

### Overall effect:
- The graph of \( f(x) \) is first reflected across the y-axis, then shifted downward by 1 unit to obtain \( g(x) \).

Would you like more details on transformations or further explanation?

Here are some related questions to expand on this topic:

1. What is the effect of replacing \( x \) with \( -x \) in any function?
2. How does adding or subtracting a constant affect the graph of a function?
3. What is the general formula for combining horizontal and vertical transformations?
4. Can you graph the functions \( f(x) \) and \( g(x) \) to compare the two?
5. How do transformations affect the domain and range of a function?

**Tip**: When applying multiple transformations, apply reflections and stretches first before performing shifts to ensure accuracy.

Explore the function transformation g(x) = f(-x) - 1, which involves reflecting the graph of f(x) across the y-axis and shifting it downward by 1 unit. This problem covers key concepts in function transformations and is suitable for students in Grades 9-11.

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