The function $y = f(x - 1)$ represents a horizontal shift of the original function $f(x)$. Specifically, this transformation shifts the graph of $f(x)$ to the right by 1 unit.

Explanation:

1. Function Shift: When we replace $x$ with $x - h$ inside a function (in this case, $h = 1$), the entire graph of the function shifts horizontally by $h$ units. Here, $h = 1$ means the function shifts 1 unit to the right.

2. Graph Impact: If you know the graph of $f(x)$, the graph of $f(x - 1)$ will look identical but moved 1 unit to the right. Every $x$-value on $f(x)$ is now increased by 1 for $f(x - 1)$.

3. Effect on Points: For a given point $(a, f(a))$ on $f(x)$, there will be a corresponding point $(a + 1, f(a))$ on $f(x - 1)$.

Would you like more details on how specific points are affected, or have any questions on this transformation?

---

Related Questions:

1. What happens to $f(x)$ if we shift it horizontally by 2 units?
2. How does a vertical shift affect the function $f(x)$?
3. What does $f(x + 1)$ represent in terms of graph transformation?
4. How would you reflect $f(x)$ across the y-axis?
5. How can we combine shifts and stretches in function transformations?

Tip:

When shifting functions, a positive shift inside the parentheses (like $f(x - h)$) moves the graph right, while a negative shift (like $f(x + h)$) moves it left.