1. What Is Reflection Over X-Axis?

Reflection over the x-axis is a transformation that flips a graph or point across the x-axis. For any point (x, y), its reflection is (x, -y). For a function f(x), the reflection is -f(x).

2. How Reflection Calculation Works

The reflection follows these mathematical rules:

Where:

• \( (x, y) \) — Original coordinates
• \( (x, -y) \) — Reflected coordinates
• \( f(x) \) — Original function
• \( -f(x) \) — Reflected function

Explanation: Reflection preserves the x-coordinate while negating the y-coordinate, creating a mirror image across the x-axis.

3. Applications of Reflection

Details: Reflection transformations are fundamental in computer graphics, physics (wave reflections), engineering design, and mathematical modeling of symmetric systems.

4. Using This Calculator

Tips: Enter a function f(x) to calculate its reflection. Optionally provide coordinates to see how specific points transform. Supported functions include polynomials, trigonometric, exponential, and logarithmic functions.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between reflection over x-axis and y-axis?
A: X-axis reflection changes (x,y) to (x,-y), while y-axis reflection changes (x,y) to (-x,y).

Q2: Can I reflect any type of function?
A: Yes, this works for all functions - linear, quadratic, trigonometric, exponential, etc.

Q3: How does reflection affect function properties?
A: Reflection preserves x-intercepts but changes the sign of y-intercepts and function values.

Q4: What if my function has restrictions?
A: The reflection will have the same domain but the range will be negated.

Q5: Can I reflect multiple points at once?
A: Currently, this calculator processes one point at a time for clarity.