The image shows a graph of the function $y = f(x)$ and asks what the graph of $y = f(x+3)$ represents.

Concept of the transformation:

When the function $f(x)$ is replaced by $f(x + 3)$, this represents a horizontal shift to the left by 3 units. The reason is that inside the function, adding a value to $x$ shifts the graph in the opposite direction.

So, the graph of $y = f(x + 3)$ is the same as the graph of $y = f(x)$, but shifted 3 units to the left along the x-axis.

Would you like more details or have any questions about this concept?

Here are 5 related questions to deepen understanding:

1. What happens to the graph if we have $y = f(x - 3)$?
2. How does a vertical shift affect a function, such as $y = f(x) + 3$?
3. What kind of transformation does multiplying $x$ by a constant, like $f(2x)$, produce?
4. How can you identify a vertical stretch or compression from the equation of a function?
5. What is the effect of adding a constant inside a function, such as $y = f(x) + c$?

Tip: Always remember that transformations inside the function (with $x$) affect the graph horizontally, while transformations outside affect it vertically.