The problem asks how the graph of $f(x)$ and $g(x) = f(x + 1)$ are related.

Analysis:

The function $g(x) = f(x + 1)$ represents a horizontal translation of $f(x)$. Specifically, when you add a constant to the input variable $x$, the graph shifts left. In this case, since $g(x) = f(x + 1)$, the graph of $f(x)$ is shifted 1 unit to the left to obtain $g(x)$.

Correct answer:

• d. The graph of the function $f(x)$ is translated left 1 unit to produce $g(x)$.

Would you like a detailed explanation of how translations affect graphs or have any other questions?

Here are five related questions to further your understanding:

1. What happens when $f(x)$ is replaced with $f(x - 2)$?
2. How does adding a constant to $f(x)$ (i.e., $f(x) + 3$) affect the graph?
3. What is the effect of multiplying $f(x)$ by a negative constant on the graph?
4. How would the graph change if $f(x)$ is replaced with $f(-x)$?
5. Can you describe the transformation represented by $f(x) = f(x - 1) - 2$?

Tip: Horizontal shifts in a graph are counterintuitive—adding to $x$ moves the graph left, while subtracting from $x$ moves it right.