https://file.aiquickdraw.com/mathbot/file/1730426292487p8cgxsgs.jpg

To solve this, we analyze the transformation of function \( f(x) \) to obtain \( g(x) = f(x - 3) + 4 \).

### Transformation Breakdown:
1. **Horizontal Shift**:
   - The expression \( f(x - 3) \) represents a horizontal shift.
   - Since it's \( x - 3 \), it indicates a **shift to the right by 3 units**.

2. **Vertical Shift**:
   - The \( + 4 \) outside the function indicates a vertical shift.
   - Adding 4 shifts the function **up by 4 units**.

### Answer:
Based on this analysis, the correct answer is:
- **D.** The graph of function \( f \) is shifted right 3 units and up 4 units.

Would you like further details or have any other questions?

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### Additional Questions for Practice:
1. What would the transformation \( g(x) = f(x + 2) - 5 \) do to the graph of \( f(x) \)?
2. If the function \( f(x) \) is shifted left 4 units and down 2 units, what would the transformed function equation look like?
3. How would the transformation \( g(x) = f(-x) \) affect the graph of \( f(x) \)?
4. What impact does a multiplication factor, like \( g(x) = 2f(x) \), have on the graph?
5. If \( g(x) = f(x) + c \), how does changing \( c \) affect the vertical shift of \( f(x) \)?

### Tip:
Horizontal shifts in functions are affected by changes within the parentheses (e.g., \( x - h \)), while vertical shifts depend on constants added outside the function (e.g., \( + k \)).

Which statement is true about the effects of the transformations on the graph of function f to obtain the graph of function g, where g(x) = f(x - 3) + 4?

Learn how to determine the effects of transformations on function graphs by analyzing g(x) = f(x - 3) + 4. Understand the horizontal shift to the right by 3 units and the vertical shift up by 4 units. Suitable for high school students studying algebra.

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