1. What is Net Change in Algebra 2?

The net change in a function between two points is the difference between the function's value at the end point (b) and its value at the starting point (a). It represents the overall change in the function's output over the interval [a, b].

2. How Does the Calculator Work?

The calculator uses the net change formula:

Where:

• \( f(x) \) — The function being evaluated
• \( a \) — The starting x-value
• \( b \) — The ending x-value

Explanation: The calculator first evaluates the function at point a, then at point b, and finally calculates the difference between these two values.

3. Importance of Net Change

Details: Net change is fundamental in understanding how functions behave over intervals. It's used in various applications including physics (displacement), economics (profit change), and biology (population growth).

4. Using the Calculator

Tips:

• Enter the function using standard mathematical notation (e.g., x^2 + 3x - 2)
• Use 'x' as your variable
• For exponents, use the caret symbol (^) or **
• Values a and b can be any real numbers

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between net change and average rate of change?
A: Net change gives the total difference (f(b)-f(a)), while average rate of change gives the difference per unit x ((f(b)-f(a))/(b-a)).

Q2: Can I use this for any type of function?
A: This calculator works for algebraic functions. For piecewise or more complex functions, you may need specialized tools.

Q3: How is net change related to integrals?
A: In calculus, the net change between a and b equals the definite integral of the function's derivative from a to b.

Q4: What if my function has discontinuities?
A: The net change calculation assumes the function is defined at both a and b. Results may not be meaningful at discontinuities.

Q5: Can I use trigonometric functions?
A: This basic version supports simple algebraic expressions. For advanced functions, consider using a graphing calculator.