Study Notes
The domain of a function is the complete set of possible values of the independent variable. Example: For the function y = x + 4, the domain is x ≥ -4. The range of a function is the complete set of all possible resulting values of the dependent variable after substituting the domain. Example: For the function y = x + 4, the range is y ≥ 0.
Exam Tips
Key Definitions to Remember
- The domain is the set of all possible values of the independent variable.
- The range is the set of all possible values of the dependent variable after substituting the domain.
Common Confusions
- Confusing the domain with the range.
- Forgetting to check if the function can take negative values under a square root.
Typical Exam Questions
- What is the domain of y = x + 4? x ≥ -4
- What is the range of y = x + 4? y ≥ 0
- Find the domain and range of f(x) = x^2 - 4x + 5. Domain: all real numbers, Range: y ≥ -3
What Examiners Usually Test
- Understanding how to find the domain by setting conditions on x.
- Ability to determine the range by evaluating the function over the domain.