https://file.aiquickdraw.com/mathbot/file/1726996816676h8yxqzww.jpg

The image you provided contains a mathematical problem regarding transformations of functions, specifically analyzing graphs of the functions \( f(x) \) and \( g(x) \).

### Breakdown of the Problem:
1. **The Red Graph (Original Function \( f(x) \)):**
   - The red graph seems to represent the original function \( f(x) \), which is a parabola.
   - From the shape of the red curve, it's clear that the function is \( f(x) = -x^2 \), meaning it's a parabola that opens downwards and passes through the origin.

2. **The Green Graph (Transformed Function \( g(x) \)):**
   - The green graph represents the transformed version \( g(x) \).
   - The transformation appears to involve both a horizontal and vertical shift. 
   - Observing the graph, we can deduce that this is likely a transformation of the form \( g(x) = -(x - 5)^2 \), which indicates a horizontal shift to the right by 5 units.

### Analysis of Statements:
- **i. \( f(x) = -x^2 \)**: This is true. The red graph represents the original function, which is \( f(x) = -x^2 \).
- **ii. \( g(x) = -(x - 5)^2 \)**: This is true. The green graph is the result of shifting the red graph 5 units to the right.
- **iii. \( f(x) = -x^2 \) mengalami pergeseran 5 satuan ke kanan**: This is false. The function \( f(x) \) has not been shifted; it is in its original position.
- **iv. \( f(x) = -x^2 \) mengalami pergeseran 5 satuan ke kiri**: This is also false. There is no shift to the left in the red graph.
- **v. \( f(x) = -x^2 \) tidak mengalami pergeseran**: This is true. The original function remains unshifted.

### Conclusion:
The correct statements are **i, ii, and v**.

Let me know if you'd like further clarification or a deeper explanation!

---

Here are 5 related questions to expand on the topic:
1. What are the general rules for translating functions horizontally and vertically?
2. How does a horizontal shift affect the equation of a function algebraically?
3. How would the equation change if the graph were shifted 5 units to the left instead of right?
4. Can you explain how the sign of the quadratic term (positive or negative) impacts the direction the parabola opens?
5. What additional transformations (such as vertical stretching or reflection) could be applied to this function?

**Tip:** When analyzing graph transformations, always compare changes in both the \( x \)-axis (horizontal shifts) and \( y \)-axis (vertical shifts) to accurately determine the transformation applied to the original function.

Pada gambar berikut, grafik berwarna merah merupakan grafik asal f(x) dan grafik berwarna hijau merupakan grafik hasil transformasi g(x). Pernyataan yang benar adalah:

Understand how to analyze and determine the correct transformations applied to quadratic functions, specifically focusing on the function f(x) = x^2 and its transformation into g(x) = (x - 5)^2. This lesson covers function transformations, horizontal shifts, and how to correctly identify statements about graph behavior.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation