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The image provided contains the following mathematical problem in Indonesian:

"Diketahui fungsi \( f(x) = 2^{x-1} + 5 \). Jika fungsi \( f(x) \) ditranslasikan oleh \( T \left( \begin{array}{c} 4 \\ -1 \end{array} \right) \), tentukanlah hasil translasi nya."

### Translation of the question:
"Given the function \( f(x) = 2^{x-1} + 5 \). If the function \( f(x) \) is translated by the transformation \( T \left( \begin{array}{c} 4 \\ -1 \end{array} \right) \), determine the result of the translation."

### Solution:
The translation described here is a horizontal and vertical shift. The transformation vector \( T \left( \begin{array}{c} 4 \\ -1 \end{array} \right) \) indicates:
- A horizontal shift of 4 units to the right.
- A vertical shift of -1 unit downwards.

#### Step 1: Horizontal Shift
The horizontal translation of 4 units to the right affects the \( x \)-values. To reflect this, replace \( x \) with \( x - 4 \) in the function.

Thus, the new function after horizontal translation is:
\[
f(x - 4) = 2^{(x-4) - 1} + 5 = 2^{x - 5} + 5
\]

#### Step 2: Vertical Shift
The vertical translation of -1 unit affects the \( y \)-values. To reflect this, subtract 1 from the entire function.

Thus, the new function after both translations is:
\[
f_{\text{translated}}(x) = 2^{x-5} + 5 - 1 = 2^{x-5} + 4
\]

### Final Answer:
The translated function is \( f_{\text{translated}}(x) = 2^{x-5} + 4 \).

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Would you like further details or explanations?

Here are 5 related questions to consider:
1. What is the general formula for translating a function?
2. How do horizontal and vertical shifts affect the graph of exponential functions?
3. How would the graph of \( f(x) = 2^{x-1} + 5 \) look before and after translation?
4. What is the effect of shifting a function by a transformation vector \( T \left( \begin{array}{c} a \\ b \end{array} \right) \)?
5. How can you apply transformations to other types of functions, such as quadratic or trigonometric functions?

**Tip:** When applying a horizontal shift, remember that replacing \( x \) with \( x - a \) shifts the graph *right* by \( a \) units, and replacing \( x \) with \( x + a \) shifts it *left* by \( a \) units.

Diketahui fungsi f(x) = 2^(x-1) + 5. Jika fungsi f(x) ditranslasikan oleh T(4, -1), tentukanlah hasil translasi nya.

Solve the translation of the exponential function f(x) = 2^(x-1) + 5 using the transformation T(4, -1). Understand how horizontal and vertical shifts affect the function and find the translated function.

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