1. What is Reflection Over X-Axis?

Reflection over the x-axis is a transformation that flips a graph vertically across the x-axis. Each point (x, y) on the original graph becomes (x, -y) on the reflected graph.

2. How Does Reflection Work?

When reflecting over the x-axis, the x-coordinates remain unchanged while the y-coordinates change sign. This creates a mirror image of the original graph across the x-axis.

3. Mathematical Formula

The mathematical representation of reflection over the x-axis is:

Where:

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

Example: If the original function is \( y = x^2 \), the reflected function would be \( y = -x^2 \).

4. Using the Calculator

Instructions: Enter your function in terms of x (e.g., x^2, sin(x), 2*x+3), specify the x-range for graphing, and click "Calculate & Graph" to see both the original and reflected functions.

5. Frequently Asked Questions (FAQ)

Q1: What functions can I graph with this calculator?
A: You can graph polynomial, trigonometric, exponential, and other mathematical functions.

Q2: How does reflection affect function properties?
A: Reflection changes the sign of y-values, turning maxima into minima and vice versa, while x-intercepts remain unchanged.

Q3: Can I reflect over other axes?
A: Yes, reflection can also be done over the y-axis (x → -x) or origin (both x and y change sign).

Q4: What's the difference between reflection and rotation?
A: Reflection creates a mirror image, while rotation turns the graph around a point by a specific angle.

Q5: Are there functions that look the same after reflection?
A: Odd functions (f(-x) = -f(x)) are symmetric about the origin and appear similar after reflection, though not identical.