Learning Objectives
What You Should Be Able To Do
Interactive Study Tools
These tools are here to help students slow down and think about the method before rushing to an answer.
Tool 1
Study Planner
Use this to break a topic into small study sessions.
Plan: A clear breakdown will appear here.
Tool 2
Method Reminder
This quick guide reminds students what to do when they feel stuck.
- Read the story: what is the question really asking?
- Choose the method: identify the correct idea before calculating.
- Show the reason: do not skip the logic.
- Check the answer: make sure it fits the situation.
1. What is a Function?
Simple explanation: This section explains how one value can depend on another, and how to read that relationship carefully.
A function is a rule that assigns each input (Domain) to exactly one output (Range).
- Domain: The set of all possible input values (x).
- Range: The set of all resulting output values (f(x)).
2. Key Function Types
Simple explanation: This section explains how one value can depend on another, and how to read that relationship carefully.
- Linear: f(x) = mx + c (A straight line).
- Quadratic: f(x) = ax² + bx + c (A parabola).
- Composite Functions: f(g(x)) — performing one function *after* another.
- Inverse Functions: f⁻¹(x) — the "undo" operation that swaps the domain and range.
Examiner Tip
💡 Examiner Tip: To find the inverse function f⁻¹(x): 1. Replace f(x) with y. 2. Swap the x and y variables. 3. Rearrange the formula to solve for y.📝 Exam Style Questions
Simple explanation: This section explains how one value can depend on another, and how to read that relationship carefully.
Easy Q1: If f(x) = 2x + 3, find f(5).
Medium Q2: Find the inverse of f(x) = x + 4.
A1: f(5) = 2(5) + 3 = 13.
A2: y = x + 4. Swap: x = y + 4. So y = x - 4. f⁻¹(x) = x - 4.