https://file.aiquickdraw.com/mathbot/file/1727741958825dxdgu015.jpg

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.

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

Explore how the function y = f(x) transforms into y = f(x+3), resulting in a horizontal shift 3 units to the left. This explanation covers the function transformation rules and is ideal for students in Grades 9-12.

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