which equation represents the graph of y=f(x) after it is reflected in the y axis then translated horizontally 2 units to the left?

To transform the graph of \( y = f(x) \) based on the given transformations:

### Step 1: Reflect in the y-axis  
Reflection across the y-axis replaces \( x \) with \( -x \). The equation becomes:  
\[
y = f(-x)
\]

### Step 2: Translate 2 units to the left  
Translation 2 units to the left replaces \( x \) with \( x + 2 \). Applying this to \( f(-x) \), the new equation becomes:  
\[
y = f(-(x + 2))
\]

### Final Equation:
\[
y = f(-(x + 2))
\]

This is the equation that represents the graph of \( y = f(x) \) after reflecting it across the y-axis and translating it 2 units to the left.

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Do you want more details on any part of the transformations?  
Here are 5 related questions you might find interesting:

1. How do reflections across the x-axis differ from reflections across the y-axis in terms of equations?  
2. What is the effect of horizontal translations on the graph of \( y = f(x) \)?  
3. How can multiple transformations be applied in different orders?  
4. What changes would occur if the graph were translated 2 units to the **right** instead?  
5. How can the transformations be visualized step-by-step using a graph?

**Tip:** Always apply transformations in the correct sequence (e.g., reflections before translations) to avoid errors.

Which equation represents the graph of y=f(x) after it is reflected in the y-axis then translated horizontally 2 units to the left?

Learn how to find the equation of a graph after transformations, including reflection in the y-axis and horizontal translation. This solution demonstrates step-by-step transformations for y = f(x) using reflection and translation rules. Perfect for Grades 9-12 math students.

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