# Functions and graphs notes

> CAPS-aligned study notes for Functions and graphs in Grade 12 Mathematics. Browse the sections below for explanations, worked examples and exam preparation.

- Page: https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs

Breadcrumbs: [Home](https://www.hlayiso.com/) › [Grade 12](https://www.hlayiso.com/grade-12) › [Mathematics](https://www.hlayiso.com/grade-12/mathematics) › [Notes](https://www.hlayiso.com/grade-12/mathematics/notes) › [Functions and graphs](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs)

## Sections in Functions and graphs

Each entry shows the free preview (about 200 characters). Create a free Hlayiso account to read the full notes, practise every question and track your progress.

- [What is a Function?](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs/what-is-a-function) — What is a Function? Every time you calculate the cost of airtime, predict how far a car will travel, or figure out the interest on a savings account, you are working with functions. Functions…
- [Function Notation](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs/function-notation) — Function Notation When you write function notation, you are giving a function a name and clearly showing the relationship between the input and the output. Instead of writing equations with just x…
- [The Basic Functions, Formulas and Graphs](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs/the-basic-functions-formulas-and-graphs) — The Basic Functions, Formulas and Graphs In Grade 12, you must be able to identify, sketch, and analyse four families of functions: linear (straight line), quadratic (parabola), hyperbolic, and…
- [Inverse Functions](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs/inverse-functions) — Inverse Functions An inverse function reverses the operation of the original function. If $f$ takes an input and gives an output, the inverse $f^{-1}$ takes that output and returns the original…
- [The Logarithmic Function](https://www.hlayiso.com/grade-12/mathematics/notes/functions-and-graphs/the-logarithmic-function) — The Logarithmic Function The logarithmic function is the inverse of the exponential function. In the previous section, we saw that the inverse of $y = b^x$ is $y = \\log_b x$. Now we study the…

## Other Mathematics topics

- [Exponents and Surds](https://www.hlayiso.com/grade-12/mathematics/notes/exponents-and-surds)
- [Algebraic expressions, equations and inequalities](https://www.hlayiso.com/grade-12/mathematics/notes/algebraic-expressions-equations-and-inequalities)
- [Number patterns](https://www.hlayiso.com/grade-12/mathematics/notes/number-patterns)
- [Trig Functions](https://www.hlayiso.com/grade-12/mathematics/notes/trig-functions)
- [Finance, growth and decay](https://www.hlayiso.com/grade-12/mathematics/notes/finance-growth-and-decay)
- [Differential Calculus](https://www.hlayiso.com/grade-12/mathematics/notes/differential-calculus)
- [Counting principle and probability](https://www.hlayiso.com/grade-12/mathematics/notes/counting-principle-and-probability)
- [Analytical Geometry](https://www.hlayiso.com/grade-12/mathematics/notes/analytical-geometry)
- [Trigonometry](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry)
- [Trigonometry: Sine, Cosine and Area Rules](https://www.hlayiso.com/grade-12/mathematics/notes/trigonometry-sine-cosine-and-area-rules)
- [Euclidean Geometry](https://www.hlayiso.com/grade-12/mathematics/notes/euclidean-geometry)
- [Statistics](https://www.hlayiso.com/grade-12/mathematics/notes/statistics)

## Frequently asked questions

### What is covered in Functions and graphs for Grade 12 Mathematics?

The Functions and graphs section covers all key concepts from the Grade 12 Mathematics CAPS curriculum, including detailed explanations, worked examples, and exam preparation tips.

### Are the Functions and graphs notes free?

Yes. Each section has a free preview, and a free Hlayiso account lets you read the full notes.

### How do these notes help with exam preparation?

Our Functions and graphs notes are CAPS-aligned and include worked examples, common mistakes to avoid, and exam tips — everything you need to prepare for your Grade 12 Mathematics exams.

### Are there quizzes for Functions and graphs?

Yes. Hlayiso has quizzes for Functions and graphs in Grade 12 Mathematics. Test your understanding after reading the notes.

---

Hlayiso: free CAPS and IEB past papers, memos, notes and study guides for South African learners. When citing, link the page URL above, not a PDF or /api/ URL.