How to Master Functions in Grade 12 Mathematics (IEB & DBE)

Functions and graphs carry a big, very learnable chunk of Grade 12 Mathematics Paper 1 — and they're one of the most predictable topics in the whole exam. Most students can draw a parabola; the ones who get distinctions can read one. That's the gap this guide closes.

The functions you need to know cold

• Linear — straight lines, gradient and intercepts
• Quadratic — parabolas, turning point, axis of symmetry
• Hyperbola — asymptotes and the effect of shifts
• Exponential — growth/decay and its asymptote
• The inverse of each, including the log function as the inverse of the exponential

For every one of these, know its shape, its key features, and how the parameters (a, p, q) move and stretch it.

The four questions examiners always ask

Whatever the function, the questions come from the same small set. Train yourself to answer these for any graph and you've banked the marks:

1. What are the intercepts? Set y = 0 and x = 0.
2. What's the turning point or asymptote? The defining feature of the graph.
3. What's the domain and range? Especially after a transformation.
4. For which values of x is f(x) > 0, or f(x) > g(x)? The interpretation question — where most marks leak.

Cover the answer on any past-paper function question and ask yourself those four questions before you look. If you can answer them every time, you've mastered functions.

Where students lose marks

• Transformations — shifts, reflections and stretches. Practise reading "f(x − 2) + 3" as a movement, not an algebra puzzle.
• Interpreting intersections — "for which x is one graph above the other" trips people up. Sketch both, find where they cross, then read off the interval.
• Inverses — swapping x and y, and restricting the domain so the inverse is a function.

How to practise

Do every function and graph question from the last five years of IEB and DBE past papers, back to back. Patterns appear fast. Keep an error log of the specific sub-skill you missed — usually it's the interpretation part, not the sketching.

Functions are a distinction-builder because they reward method over memory. For the full picture, see our guide on how to get a distinction in Grade 12 Mathematics, and if a specific transformation or inverse still isn't clicking, book a tutor who can work through it with you.