Give me expression of f(x) when it shifted right on x axis 1 unit, reflected in y axis, then stretched parallel to y axis scale factor 2

To determine the expression for \( f(x) \) when it undergoes the specified transformations, we apply them in the following order:

### Transformations:
1. **Shift right on the x-axis by 1 unit**:
   Replace \( x \) with \( x - 1 \), so \( f(x) \) becomes \( f(x - 1) \).

2. **Reflect in the y-axis**:
   Replace \( x \) with \( -x \), so \( f(x - 1) \) becomes \( f(-(x - 1)) \).

3. **Stretch parallel to the y-axis with a scale factor of 2**:
   Multiply the entire function by 2, so \( f(-(x - 1)) \) becomes \( 2f(-(x - 1)) \).

### Final Expression:
The resulting function is:
\[
g(x) = 2f(-(x - 1))
\]

Would you like further clarification or examples to understand these transformations? Here are some related questions to deepen your understanding:

1. How does a shift left on the x-axis by 2 units affect the function's expression?
2. What is the effect of reflecting a function in the x-axis instead of the y-axis?
3. Can you combine multiple stretches (e.g., by different scale factors along x and y)?
4. How do you identify transformations when analyzing a graph?
5. What happens when you apply a horizontal compression with a reflection?

**Tip:** When working with transformations, apply them step by step, and keep track of the order to avoid confusion.

Discover how to transform the function f(x) by shifting it right 1 unit, reflecting it in the y-axis, and stretching it vertically with a scale factor of 2. This step-by-step guide explains function transformations and their mathematical expressions. Ideal for Grades 10-12 students.

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