1. What is Domain and Range?

The domain of a function is the set of all possible input values (x-values) for which the function is defined, while the range is the set of all possible output values (f(x)-values) that the function can produce.

2. How Does the Calculator Work?

The calculator analyzes the mathematical function to determine:

Explanation: Different function types have different domain and range characteristics:

• Polynomials: Typically domain = all real numbers
• Rational functions: Exclude values that make denominator zero
• Square root functions: Require radicand ≥ 0
• Trigonometric functions: Have specific range limitations

3. Importance of Domain and Range

Details: Understanding domain and range is essential for:

• Determining where a function is valid
• Graphing functions accurately
• Solving equations and inequalities
• Understanding function behavior

4. Using the Calculator

Tips: Enter the function using standard mathematical notation:

• Use 'x' as the variable
• For exponents, use ^ (e.g., x^2)
• For square roots, use sqrt()
• For fractions, use parentheses (e.g., 1/(x+2))

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between domain and range?
A: Domain refers to all possible input values (x-values), while range refers to all possible output values (f(x)-values).

Q2: How do you find domain and range without a calculator?
A: For domain, identify values that would make the function undefined. For range, analyze the function's behavior and limitations.

Q3: Can a function have an empty domain?
A: Yes, if there are no real numbers that satisfy the function's requirements (e.g., sqrt(x) when x < 0 in real numbers).

Q4: Are domain and range always continuous intervals?
A: No, they can be discrete points or combinations of intervals and discrete points.

Q5: How does composition affect domain and range?
A: The domain of a composite function is restricted by both the inner and outer functions' domains.