The graphs of $f(x) = x$ and $g(x) = f(x) + 3$ are related through a vertical translation.

• Graph of $f(x) = x$: This is a straight line that passes through the origin with a slope of 1, forming a 45-degree angle with the x-axis.

• Graph of $g(x) = f(x) + 3 = x + 3$: This is also a straight line with the same slope of 1, but the entire graph is shifted 3 units upward compared to the graph of $f(x)$.

In other words, every point on the graph of $f(x) = x$ is translated vertically by 3 units to form the graph of $g(x) = x + 3$. The shape and slope of the two lines are the same; only their vertical positions differ.

Would you like further clarification or more details on graph transformations?

---

Here are five follow-up questions to deepen your understanding:

1. What would happen if we added a negative constant to $f(x)$ instead of a positive one?
2. How would the graph change if $g(x) = f(x) - 3$?
3. Can you describe how the slope affects the orientation of the graph?
4. How would the graphs change if we multiplied $f(x)$ by a constant instead of adding one?
5. What is the y-intercept of the graph of $g(x)$?

Tip: When shifting graphs, adding a constant moves the graph vertically, while adding inside the function argument affects horizontal shifts.