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The question from the image is:

> **Diketahui fungsi** \( f(x) = x^2 + 3x - 4 \). **Jika dilakukan translasi terhadap grafik fungsi tersebut dengan vektor** \( T(2,1) \), **tentukan persamaan fungsi bayangan.**

### Translation of the question:

"Given the function \( f(x) = x^2 + 3x - 4 \). If a translation is performed on the graph of this function with the vector \( T(2,1) \), determine the equation of the transformed function."

### Solution:

A translation of a function involves shifting the graph horizontally and/or vertically. A translation vector \( T(2,1) \) means:
- A horizontal shift of \( +2 \) (rightward by 2 units),
- A vertical shift of \( +1 \) (upward by 1 unit).

To translate a function \( f(x) \) horizontally by \( h \) and vertically by \( k \), the transformation is given by:

\[
f'(x) = f(x - h) + k
\]

In this case:
- \( h = 2 \),
- \( k = 1 \).

So, the transformed function is:

\[
f'(x) = f(x - 2) + 1
\]

#### Step 1: Calculate \( f(x - 2) \)

The original function is:

\[
f(x) = x^2 + 3x - 4
\]

Now substitute \( x - 2 \) into this function:

\[
f(x - 2) = (x - 2)^2 + 3(x - 2) - 4
\]

#### Step 2: Expand the expression

\[
(x - 2)^2 = x^2 - 4x + 4
\]
\[
3(x - 2) = 3x - 6
\]

Now substitute these back:

\[
f(x - 2) = x^2 - 4x + 4 + 3x - 6 - 4
\]
\[
f(x - 2) = x^2 - 4x + 3x + 4 - 6 - 4
\]
\[
f(x - 2) = x^2 - x - 6
\]

#### Step 3: Add the vertical shift (+1)

\[
f'(x) = f(x - 2) + 1 = x^2 - x - 6 + 1
\]
\[
f'(x) = x^2 - x - 5
\]

### Final Answer:

The equation of the transformed function is:

\[
f'(x) = x^2 - x - 5
\]

Would you like a more detailed explanation on any of the steps?

---

### Related Questions:
1. What happens if the translation vector is \( T(-2,-1) \)?
2. How would you translate the function vertically by 3 units?
3. How do you reflect a function across the x-axis?
4. What is the difference between horizontal and vertical translations?
5. How can we shift a function both vertically and horizontally by arbitrary values?

### Tip:
For horizontal shifts, remember to modify the input of the function, \( f(x - h) \), where \( h \) is the shift. For vertical shifts, simply adjust the output by adding or subtracting a constant value.

Diketahui fungsi f(x) = x^2 + 3x - 4. Jika dilakukan translasi terhadap grafik fungsi tersebut dengan vektor T(2,1), tentukan persamaan fungsi bayangan.

Learn how to translate the function f(x) = x^2 + 3x - 4 by the vector T(2,1). This solution covers key algebraic concepts, including function translations, horizontal and vertical shifts. Suitable for students in Grades 9-11.

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