# Maths: Functions and graphs

> 13 questions based on past NSC papers, on functions and graphs, 29 marks in our Paper 1 questions. Answer one and see it marked mark by mark.

Canonical: https://sharpkop.co.za/maths/functions-and-graphs/
Last updated: 2026-11-12

## Questions

- [Nov 2024 · Paper 1 · Q4.1 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q4-1/): The function g is defined by g(x) = b^x + 2, where b > 0. The point P(3; 43/8) lies on the graph of g. Calculate the value of b.
- [Nov 2024 · Paper 1 · Q4.2 (1 mark)](https://sharpkop.co.za/maths/2024-nov-p1/q4-2/): The function g(x) = b^x + 3 is defined for b > 0, and the point P(2; 37/4) lies on g.
- [Nov 2024 · Paper 1 · Q4.3 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q4-3/): The function g is defined by g(x) = b^x - 2 where b > 0. The point P(2; -7/4) lies on g.
- [Nov 2024 · Paper 1 · Q4.4 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q4-4/): The function f(x)=(1/2)^x-1 is given. C is the point on the graph of f where y=7.
- [Nov 2024 · Paper 1 · Q5.1 (1 mark)](https://sharpkop.co.za/maths/2024-nov-p1/q5-1/): The diagram below shows the graph of f(x) = a/(x + p) + q with domain x ∈ R, x ≠ 2. Write down the value of p.
- [Nov 2024 · Paper 1 · Q5.2 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q5-2/): The diagram below shows the graph of f(x)=a/(x+p)+q with domain (-∞;2)cup(2;∞). The graph of f cuts the y-axis at (0;2).
- [Nov 2024 · Paper 1 · Q5.3 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q5-3/): The diagram below shows the graph of f(x)=a/(x+p)+q, with domain xinR, x ≠ 2. The vertical asymptote is x=2 and the horizontal asymptote...
- [Nov 2024 · Paper 1 · Q5.4 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q5-4/): The graph of f(x)=(-6)/(x-2)-2 is drawn in the diagram below. Its domain is x ∈ (-∞;2)cup(2;∞).
- [Nov 2024 · Paper 1 · Q5.5 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q5-5/): The function f is given in the information above. Graph f is transformed to a new graph h so that: • h has the same domain and the same...
- [Nov 2024 · Paper 1 · Q6.1 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q6-1/): The diagram below shows the graph of f(x) = -x^2 + 6x + 7, a parabola with turning point B. Calculate the coordinates of B.
- [Nov 2024 · Paper 1 · Q6.2 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q6-2/): The diagram below shows the parabola f(x) = -x^2 + 2x + 8 and a straight line g.
- [Nov 2024 · Paper 1 · Q8.3.2 (1 mark)](https://sharpkop.co.za/maths/2024-nov-p1/q8-3-2/): The function g is defined by g(x) = -4x^2. State one way to restrict the domain of g so that its inverse, g^(-1), is a function.
- [Nov 2024 · Paper 1 · Q8.3.3 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q8-3-3/): The function g is defined by g(x) = -4x^2. Find the inverse relation of g and write it as y = …, choosing the branch for which y ≤ 0.

## Related

- [Grade 12 Maths past papers](https://sharpkop.co.za/maths/)

Questions are based on National Senior Certificate papers set by the Department of Basic Education. Sharpkop is not affiliated with or endorsed by the Department.