https://r2.erweima.ai/mathbot/image/172642779473035yccu66.jpg

The image you've provided includes a graph and some equations in Persian, along with a problem description. I'll translate the text and explain the mathematical concept.

### Translated text:
The problem asks something along the lines of:

"Which of the following equations corresponds to the reflected version of the function in the given graph?"

The graph seems to show a reflection of some lines, and the options given below are different equations in the format:
1. \( y = x + 0.1 \)
2. \( y = -x + 0.1 \)
3. \( y = x - 0.1 \)
4. \( y = -x - 0.1 \)

### Analysis:
The graph appears to illustrate a reflection of lines across the axes or some symmetry. The task is to match the appropriate reflection with the corresponding equation.

Reflections of lines typically occur in the following cases:
1. **Reflection over the y-axis**: This changes the slope from positive to negative. For example, \( y = x \) becomes \( y = -x \).
2. **Vertical shifts**: The constant value changes, such as \( y = x + c \) being shifted vertically by \( c \).

To match the correct equation to the reflection, you need to analyze the graph and determine whether the line is reflected over the y-axis (which would switch the sign of the slope) or if it's only shifted.

### Would you like further details or have any questions about this process? Here are 5 related questions:

1. What happens to the equation of a line when it is reflected over the x-axis?
2. How would you reflect a line over the y-axis algebraically?
3. How do vertical shifts affect the graph of a linear equation?
4. What is the relationship between the slope of a line and its reflection?
5. How can you confirm which equation matches the given graph?

**Tip:** Always remember that reflections flip the direction of the slope, while translations shift the graph up or down (or left/right for horizontal shifts).

Which of the following equations corresponds to the reflected version of the function in the given graph?

Analyze the graph and find the correct reflected equation from a set of linear equations. This exercise focuses on understanding the reflection of functions, using the slope-intercept form and reflections across axes.

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