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The problem involves transforming the function \( y = x + 10 \) through two translations. Let me explain the process step by step:

We are given two translation vectors:
1. \( T_1 = \begin{pmatrix} 1 \\ 2 \end{pmatrix} \)
2. \( T_2 = \begin{pmatrix} 3 \\ 4 \end{pmatrix} \)

### Step 1: Apply the first translation \( T_1 \)
The translation vector \( T_1 = \begin{pmatrix} 1 \\ 2 \end{pmatrix} \) means that we shift the graph of the function by 1 unit in the x-direction and 2 units in the y-direction.

The original function is:
\[
y = x + 10
\]

After applying the first translation, the new coordinates will be:
\[
x' = x + 1
\]
\[
y' = y + 2
\]
Substituting \( y = x + 10 \) into this, we get:
\[
y' = (x + 1) + 10 + 2 = x + 11 + 2 = x + 13
\]
So, after the first translation, the new function is:
\[
y = x + 13
\]

### Step 2: Apply the second translation \( T_2 \)
Now, apply the second translation vector \( T_2 = \begin{pmatrix} 3 \\ 4 \end{pmatrix} \), which translates the graph by 3 units in the x-direction and 4 units in the y-direction.

Thus:
\[
x'' = x + 3
\]
\[
y'' = y + 4
\]

Starting with the function \( y = x + 13 \) from the previous step, substitute and perform the translation:
\[
y'' = (x + 3) + 13 + 4 = x + 16 + 4 = x + 17
\]

### Final result:
After both translations, the final equation of the transformed function is:
\[
y = x + 17
\]

Would you like more details on this process or have any questions?

### Related Questions:
1. What is the geometric meaning of translating a function by a vector?
2. How would the translation affect a quadratic function like \( y = x^2 + 5 \)?
3. Can multiple translations be combined into a single translation?
4. How would the function change if the translation vectors were reversed?
5. What if we apply a reflection instead of a translation?

### Tip:
Translations only affect the position of the graph, not its shape. The slope remains the same when dealing with linear equations.

Fungsi y = x + 10 ditransformasikan dengan translasi T1 = (1, 2) dilanjutkan dengan T2 = (3, 4). Tentukan hasil dari transformasi tersebut!

Learn how to transform the linear function y = x + 10 using two translation vectors T1 = (1, 2) and T2 = (3, 4). This solution covers function translation concepts in coordinate geometry, providing a step-by-step solution. Suitable for students in Grades 10-11.

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