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Linear, quadratic, hyperbolic, exponential and logarithmic functions — sketching and interpreting.
Watch the full lesson before attempting practice questions.
Master these ideas before attempting exam questions.
Domain: all allowed x-values. Range: all resulting y-values. Always state restrictions clearly.
Swap x and y, then make y the subject. Restrict the domain so the inverse is also a function.
y = a(x−p)² + q. Vertex at (p, q). Axis of symmetry: x = p. Direction determined by sign of a.
y = a/(x−p) + q. Asymptotes at x = p (vertical) and y = q (horizontal).
y = a·bˣ + q and y = logb(x). These are inverses of each other. Focus on shifts and reflections.
Commit these to memory — they appear in almost every exam.
These are your learning targets for Functions & Graphs.
Avoid these errors — they cost marks every year.
Identify which variable is restricted. Domain → x. Range → y.
Read p and q carefully from the equation. Both shift the asymptotes.
Without a domain restriction, the inverse may not be a function.
Request CAPS-aligned study materials for Functions & Graphs.
Comprehensive CAPS-aligned notes covering all key concepts, theorems, and worked examples for Functions & Graphs.
NSC-style exam questions with full memorandum. Ideal for timed practice and self-assessment before exams.
Graded practice questions organised by difficulty. Perfect for building confidence before Paper 1.
Straight answers to common Grade 12 CAPS questions about Functions and Graphs.
Functions and Graphs in Grade 12 CAPS focuses on interpreting, sketching, and analysing different graphs such as linear, quadratic, hyperbolic, and exponential functions. You also study turning points, intercepts, asymptotes, and domain and range.
Learn the features of each graph type, practise sketching from equations, and always label key points clearly. Repeating graph transformation and interpretation questions helps you improve fast.
Common mistakes include mixing up transformations, missing intercepts, drawing inaccurate asymptotes, and not reading scale properly. Many learners also forget to state domain and range correctly.
CAPS exams often test graph sketching, transformations, intersections, and interpretation of function behaviour. These questions usually appear in Paper 1 and can carry a high mark allocation.
Book a focused session with Chris Khomo and work through this topic step by step — at your own pace, online, from anywhere in South Africa.