Functions and graph sketching.
Use domains, transformations, algebra and calculus together to analyse functions and produce trustworthy sketches.
Work through the topic
Learn the method, follow the examples, then try the worksheet.
- 01
Composition and domain restrictions
Build a composite function and keep every domain restriction.
- 02
One-to-one functions
Decide whether different inputs can produce the same output.
- 03
Inverse functions and restricted domains
Find inverse rules and choose branches consistently with the original domain.
- 04
Absolute-value graphs
Interpret absolute values as transformations of inputs or outputs.
- 05
Reciprocal/composite transformations
Sketch reciprocals and compositions using sign, zeros and asymptotes.
- 06
Rational functions
Analyse rational expressions without losing holes, poles or end behaviour.
- 07
Intercepts, stationary behaviour and asymptotes
Combine intercepts, derivative signs and asymptotes into a consistent sketch.
- 08
Combining graphical/algebraic/calculus information in sketches
Produce a complete graph using mutually consistent algebraic and calculus evidence.
Topic review
Revisit the key ideas, then choose a practice paper.