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Let's work through the questions in the image you've provided. It's a set of mathematics multiple-choice questions in Indonesian related to transformations, reflections, and rotations of functions and lines.

Here are the translations and solutions for some of the questions:

### 1. Diketahui fungsi \( y = 3x^2 - 4 \) ditranslasikan oleh \( \binom{0}{3} \).
The translation vector is \( (0, 3) \), meaning that the function is shifted 3 units upwards.

**Original function:**  
\( y = 3x^2 - 4 \)

**After translation:**  
The new function will be \( y = 3x^2 - 4 + 3 \), which simplifies to:
\[
y = 3x^2 - 1
\]

**Correct answer:** a) \( y = 3x^2 - 1 \)

### 2. Garis \( m: 4x - 2y + 12 = 0 \) digeser 2 satuan ke kiri.
The translation is to the left by 2 units, meaning that \( x \) will be replaced by \( x + 2 \) in the equation.

**Original equation:**  
\( 4x - 2y + 12 = 0 \)

**Substitute \( x \) with \( x + 2 \):**
\[
4(x + 2) - 2y + 12 = 0
\]
\[
4x + 8 - 2y + 12 = 0
\]
\[
4x - 2y + 20 = 0
\]

**Correct answer:** c) \( 4x - 2y + 20 = 0 \)

### 3. Garis digeser 1 satuan ke bawah menghasilkan garis \( g': 3x - 2y - 11 = 0 \).
This indicates a downward shift by 1 unit, which means that \( y \) will be replaced by \( y - 1 \).

**Original equation:**  
\( 3x - 2y - 11 = 0 \)

**Substitute \( y \) with \( y - 1 \):**
\[
3x - 2(y - 1) - 11 = 0
\]
\[
3x - 2y + 2 - 11 = 0
\]
\[
3x - 2y - 9 = 0
\]

**Correct answer:** d) \( 3x - 2y - 9 = 0 \)

### 4. Garis \( p: 3x + 4y + 12 = 0 \) direfleksikan terhadap sumbu Y.
To reflect a line over the y-axis, replace \( x \) with \( -x \).

**Original equation:**  
\( 3x + 4y + 12 = 0 \)

**Substitute \( x \) with \( -x \):**
\[
3(-x) + 4y + 12 = 0
\]
\[
-3x + 4y + 12 = 0
\]

**Correct answer:** b) \( -3x + 4y + 12 = 0 \)

### 5. Rumus fungsi \( y = 2^{x+1} - 4 \) direfleksikan terhadap sumbu X.
To reflect a function over the x-axis, multiply the entire function by -1.

**Original function:**  
\( y = 2^{x+1} - 4 \)

**After reflection:**  
\[
y = -(2^{x+1} - 4)
\]
\[
y = -2^{x+1} + 4
\]

**Correct answer:** d) \( y = -2^{x+1} + 4 \)

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Would you like further details on any specific questions, or assistance with the remaining problems? Here are five follow-up questions you might find helpful:

1. How would you reflect a function over the y-axis instead of the x-axis?
2. What is the difference between a translation and a reflection in mathematical transformations?
3. Can you explain how rotations of functions around a point work?
4. How does translating a line affect its equation?
5. What is the effect of rotating a line by 180 degrees around the origin?

**Tip:** When working with transformations, always identify whether the change is in the \( x \)-direction or \( y \)-direction to apply the correct substitution or adjustment.

The problem consists of a set of multiple-choice questions related to transformations, reflections, rotations, and dilations of functions and lines, all in the context of algebra.

Explore detailed solutions for algebra problems involving translations, reflections, and rotations of functions and lines. This guide covers the essential transformation formulas, reflection theorems, and more, suitable for high school students in Grades 10-12.

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