Functions & Graphs Formula Sheet (Grade 12 CAPS)

Standard forms, turning points, asymptotes, inverses and transformation rules for Grade 12 CAPS functions and graphs, with NSC Paper 1 exam notes.

Functions carry roughly 35 marks of NSC Paper 1. The standard forms below let you read intercepts, asymptotes and turning points directly off an equation.

Formulas

Formula	Expression	Note
Parabola turning point form	`y = a(x − p)² + q`	Turning point is (p; q); axis of symmetry x = p.
Parabola axis of symmetry	`x = −b/2a`	Substitute back to get the y-value of the turning point.
Hyperbola	`y = a/(x − p) + q`	Asymptotes x = p and y = q; axes of symmetry y = ±(x − p) + q.
Exponential function	`y = a·b^(x − p) + q`	Horizontal asymptote y = q; b > 0 and b ≠ 1.
Logarithmic inverse	`y = log_b x ⇔ x = b^y`	Inverse of the exponential graph; reflect in y = x.
Average gradient	`m = (y₂ − y₁)/(x₂ − x₁)`	Gradient of the straight line joining two points on a curve.

How to use them

Label intercepts, asymptotes and turning points on every sketch — they are separate marks.
For inverses, swap x and y first, then make y the subject.
Restrict the domain when asked for an inverse that must be a function.
Worked example: y = −2(x − 1)² + 8 has turning point (1; 8), a maximum because a < 0, so the range is y ≤ 8. Its x-intercepts satisfy (x − 1)² = 4, so x = 3 or x = −1.

Frequently asked questions

Are all Functions & Graphs formulas given in the NSC exam?

Some are printed on the official information sheet, but not all. Treat every formula on this page as examinable and learn it with a worked example so you recognise when to use it.

Which NSC paper tests Functions & Graphs?

Functions & Graphs is examined in Paper 1 of the NSC Mathematics examination.

How do I practise these formulas?

Snap a functions & graphs question into the Snap&Learn AI solver — it shows the substitution and every method mark the way the NSC memo does.

Snap&Learn gives South African Matric learners instant, CAPS-aligned, step-by-step Mathematics solutions. Snap or upload a question and the AI shows every method mark the way the NSC memo awards them. Your first three AI solutions are free.