Study Notes
Functions are mathematical correspondences where each element of a set X is associated with exactly one element of a set Y. Functions can be one-one or many-one, and they can be combined or inverted to form new functions. Transformations such as translations, reflections, and stretches can alter the graph of a function.
Exam Tips
Key Definitions to Remember
- Function — A correspondence associating each element of a set X with exactly one element of a set Y.
- One-one Function — Each element of a set X associates with a unique element of a set Y.
- Inverse Function — A function that reverses the operation of the original function.
- Composite Function — A function formed by applying one function to the results of another.
Common Confusions
- Confusing the domain with the range.
- Assuming all functions have inverses.
- Mixing up the order of operations in composite functions.
Typical Exam Questions
- What is the range of the function f(x) = x² + 1 for x ∈ {-1, 0, 1, 2}? The range is {1, 2, 5}.
- Is the function f(x) = x² + 1 a one-one function? No, because both -1 and 1 map to 2.
- How do you find the inverse of a function? Swap x and y in the equation and solve for y.
What Examiners Usually Test
- Understanding of function definitions and properties.
- Ability to find and interpret the range and domain.
- Skill in performing and understanding transformations on graphs.
- Competence in finding and verifying inverse functions.