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### Given Information:
1. The linear function \( f(x) = 10x - 2 \) and exponential function \( g(x) = 3^x - 1 + 4 \).
2. The function \( f(x) \) is transformed by the translation \( T = \binom{5}{5} \), resulting in \( f'(x) \).
3. The function \( g(x) \) is transformed by the translation \( T = \binom{2}{2} \), resulting in \( g'(x) \).
4. Translation \( T = \binom{6}{-1} \) is applied to the function \( f(x) \) to form the function \( h(x) \).

Now, let's go through the questions:

### Question 1:
The transformation of \( f(x) \) by the translation \( T = \binom{5}{5} \).

The transformation involves translating the function vertically by 5 units and horizontally by 5 units. So, we apply the transformation to \( f(x) \) as follows:
\[
f'(x) = f(x - 5) + 5
\]
Substitute \( f(x) = 10x - 2 \) into the above equation:
\[
f'(x) = 10(x - 5) - 2 + 5
\]
\[
f'(x) = 10x - 50 - 2 + 5
\]
\[
f'(x) = 10x - 47
\]
Thus, the correct answer for question 1 is **b. \( f'(x) = 10x - 47 \)**.

### Question 2:
Evaluate \( f'(x) \) for specific values of \( x \).

From the previous transformation, we know \( f'(x) = 10x - 47 \).

- \( f'(2) = 10(2) - 47 = 20 - 47 = -27 \)
- \( f'(3) = 10(3) - 47 = 30 - 47 = -17 \)
- \( f'(4) = 10(4) - 47 = 40 - 47 = -7 \)
- \( f'(5) = 10(5) - 47 = 50 - 47 = 3 \)

The correct values are:
- \( f'(2) = -27 \)
- \( f'(3) = -17 \)
- \( f'(4) = -7 \)
- \( f'(5) = 3 \)

### Question 3:
The transformation of \( g(x) \) by the translation \( T = \binom{2}{2} \).

Apply the translation to \( g(x) = 3^x + 3 \):
\[
g'(x) = g(x - 2) + 2
\]
Substitute \( g(x) = 3^x + 3 \):
\[
g'(x) = 3^{(x - 2)} + 3 + 2
\]
\[
g'(x) = 3^{x - 2} + 5
\]
Thus, the correct answer for question 3 is \( g'(x) = 3^{x - 2} + 5 \).

### Question 4:
Determine the truth of the following statements based on the function \( g'(x) = 3^{x - 2} + 5 \):

1. \( g'(0) = \frac{6}{27} \) is **True**.
   - \( g'(0) = 3^{0 - 2} + 5 = 3^{-2} + 5 = \frac{1}{9} + 5 = \frac{46}{9} \).

2. \( g'(1) = \frac{6}{9} \) is **True**.
   - \( g'(1) = 3^1 Touch

Given a linear function f(x) = 10x - 2 and an exponential function g(x) = 3^x - 1 + 4, transformations involving translations are applied. For example, f(x) is transformed with T = (5,5) to produce f'(x), and g(x) is transformed with T = (2,2) to produce g'(x). Additionally, a new transformation T = (6, -1) is applied to f(x) to produce h(x). Solve related questions about the transformed functions and evaluate specific values.

This problem involves transforming linear and exponential functions using translations. It covers key algebraic concepts, such as transforming f(x) = 10x - 2 and g(x) = 3^x + 3, and calculating specific function values post-transformation. Ideal for students in Grades 10-12.

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