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.