Explore different types of functions and their properties
Functions describe relationships between variables and are fundamental to mathematics. This section covers linear, quadratic, exponential, and hyperbolic functions. Each topic includes interactive games and quizzes to test your understanding.
Select a function type to begin your studies.
y = mx + c - Straight line graphs, slope, intercepts, parallel and perpendicular lines
Explore Lineary = ax² + bx + c - Parabolas, vertex, axis of symmetry, roots
Explore Quadraticy = a·bxˣ - Growth and decay, asymptotes, applications
Explore Exponentialy = a/(x + p) + q - Asymptotes, domain, range, branches
Explore Hyperbolic| Function Type | General Form | Key Features |
|---|---|---|
| Linear | y = mx + c | Slope m, y-intercept c, constant rate of change |
| Quadratic | y = ax² + bx + c | Parabola, vertex (-b/2a,..), axis of symmetry |
| Exponential | y = a·bxˣ | Asymptote y = 0, growth (b>1) or decay (0 |
| Hyperbolic | y = a/(x + p) + q | Vertical asymptote x = -p, horizontal asymptote y = q |
Test your understanding of functions before diving into the topics.
Hint: Think about the basic properties of each function type.
Use this Functions section to learn how equations, tables, graphs, gradients, intercepts, asymptotes, and turning points describe relationships. Move between algebra and graph interpretation until you can explain what each feature means.
For every function, practise reading the equation, sketching the basic shape, and identifying the important points before attempting exam questions.
A useful path from this page is to begin with Linear Functions, continue with Quadratic Functions, and then test your understanding with Exponential Functions. Do not rush through the links; spend time on the examples and make sure you can explain the main idea without looking at the notes.
Use this page to build definitions, worked examples, formulas, diagrams, and problem-solving methods. Write down key terms, formulas, diagrams, or steps that appear often so that revision becomes active instead of just rereading.
Keep a correction book for sign errors, formula mistakes, geometry reasons, and questions that need more practice. After each lesson, close the page and try a short self-test from memory before checking your notes again.
If you are stuck, start with algebra basics and number skills, because many later topics depend on accurate manipulation and clear working. If a topic feels too difficult, return to the previous link, revise the basics, and then try the examples again before using past papers.
