1. What is a Function Calculator?

A function calculator computes the value of a mathematical function for a given input (n). It can handle various types of functions including linear, quadratic, and exponential functions.

2. How Does the Calculator Work?

The calculator evaluates functions based on their type:

Where:

• \( n \) — The term number (input value)
• \( a, b, c \) — Coefficients of the function
• \( r \) — Common ratio for exponential functions

Explanation: The calculator evaluates the function at the specified point n using the appropriate mathematical formula.

3. Importance of Function Calculation

Details: Calculating function values is fundamental in mathematics, physics, engineering, and computer science for modeling relationships between quantities.

4. Using the Calculator

Tips: Select the function type and enter the term number n. The calculator will compute f(n) based on example functions (you can modify the PHP code to implement your specific functions).

5. Frequently Asked Questions (FAQ)

Q1: What types of functions can this calculator handle?
A: Currently linear, quadratic, and exponential functions are supported. The code can be extended for other function types.

Q2: Can I input negative values for n?
A: The calculator accepts non-negative integers (n ≥ 0) by default, but this can be modified in the code.

Q3: How can I add my own custom function?
A: Edit the PHP code to include your function's formula in the switch-case statement.

Q4: What's the maximum value of n I can input?
A: The calculator can handle very large numbers, but extremely large values may cause computational limitations.

Q5: Can this calculator handle recursive functions?
A: The current implementation calculates direct formulas. Recursive functions would require additional programming.