Functions practice, graded like a real exam
Injective, surjective, bijective, composition, inverse. Functions rewards precision and repetition more than almost anything else on a sets, relations & functions course — it is exactly the kind of topic where working through twenty varied problems beats re-reading the chapter a third time. QED gives you an endless supply of exam-grade functions questions and marks every answer the way an examiner would, so each attempt actually teaches you something.
✓ First questions free · no card · no personal data stored
What you'll practise in Functions
- Domain, codomain, image & preimage
- Injective / surjective / bijective
- Composition g∘f and its properties
- Inverse functions
- Counting functions between finite sets; cardinality
What a Functions question looks like
In a QED session, an exam-level functions question might ask you to classify a function as injective, surjective or bijective with a proof or a counterexample, compute a composition, or find an inverse.
Every question carries a hidden marking rubric. You answer in real notation, and QED marks each criterion separately — awarding partial credit and showing a full worked solution, so you learn from the marks you dropped.
Why students use QED for Functions
Not another chatbot that blesses whatever you type. QED is built for deliberate practice — the way maths actually sticks.
Practice that never runs out
A textbook gives you a handful of functions exercises with the same worked answers everyone has seen. QED generates unlimited fresh functions questions at warm-up, exam and challenge level, so you can drill a weak spot until it is automatic — not until you run out of problems.
Marked like an examiner, not a checkbox
Most tools just say “correct” or “wrong”. QED marks your functions answer against a point-by-point rubric, awards partial credit, shows exactly where the reasoning slipped, and gives a full model solution. A right answer with the wrong argument still loses the argument marks — just like a real exam.
A library you can come back to
Every functions question you generate is saved, organised and re-takeable as a timed exam. Your mastery is tracked per topic, so you always know whether Functions is exam-ready or still needs work — and you can export any question or exam report to PDF.
Write maths the way you actually write it
Answer in real notation with a one-tap symbol palette and a visual equation editor, drop in truth tables, or photograph a handwritten page — QED converts your handwriting to clean LaTeX. No fighting with syntax to show what you know.
How practising Functions works
- Generate a fresh questionPick Functions and a difficulty — warm-up to build intuition, exam level for the real thing, or challenge for multi-step problems. A new, verified question appears in seconds.
- Answer in real notationType it, build it in the equation editor, lay out a truth table, or photograph your handwritten working and let QED convert it to LaTeX.
- Get marked criterion by criterionQED scores every rubric point separately, awards partial credit, flags where the reasoning slipped and shows a full model solution. The question is saved to your library to retake any time.
Related topics
Building a full picture of sets, relations & functions? These pair naturally with Functions.
Functions — frequently asked questions
Is QED good for revising Functions before an exam?
Yes — that is exactly what it is built for. Generate functions questions at exam level (or push up to challenge), answer them under timed exam mode, and get marked against a rubric with a full model solution. You can retake any question and watch your Functions mastery climb until it is solid.
How many Functions questions can I practise?
As many as you like. QED generates fresh functions problems on demand instead of recycling a fixed set, and every question you make is saved to your library to retake for free. New accounts start with free question generations, no card required.
Do I need to know LaTeX to answer Functions questions?
No. There is a one-tap palette for symbols, a visual equation editor, and a truth-table builder — and you can photograph a handwritten solution and let QED convert it to LaTeX for you. You concentrate on the maths, not the typesetting.
Ready to make Functions exam-proof?
Generate your first functions questions free — no card, no setup, no personal data stored. Practise until it is second nature.
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