1. What is the Reflection Rule Equation?

The reflection rule equation \( y = -f(x) \) represents a transformation that reflects a function across the x-axis. This mathematical operation changes the sign of all y-values while keeping x-values unchanged.

2. How Does the Calculator Work?

The calculator applies the reflection rule:

Where:

• \( f(x) \) — Original function
• \( -f(x) \) — Reflected function across x-axis

Explanation: The reflection transformation multiplies the output of the function by -1, effectively mirroring the graph across the x-axis.

3. Importance of Reflection Transformation

Details: Reflection transformations are fundamental in coordinate geometry and function analysis. They help understand symmetry properties and are used in various applications including computer graphics, physics, and engineering.

4. Using the Calculator

Tips: Enter your function f(x) using standard mathematical notation. You can optionally provide an x-value to calculate both the original and reflected function values at that point.

5. Frequently Asked Questions (FAQ)

Q1: What types of functions can I input?
A: You can input polynomial, trigonometric, exponential, and other standard mathematical functions using proper notation.

Q2: How does reflection differ from other transformations?
A: Reflection specifically mirrors the graph across an axis, while translation moves it and scaling changes its size.

Q3: Can I reflect across the y-axis instead?
A: Yes, reflection across y-axis uses the equation \( y = f(-x) \), which is a different transformation.

Q4: What happens to function properties after reflection?
A: Domain remains unchanged, range is multiplied by -1, and symmetry properties may be altered.

Q5: Are there limitations to this calculator?
A: The calculator handles standard mathematical expressions. Complex functions or undefined operations may require specialized mathematical software.