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?

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., $+ k$).