Module 2 · Algebra
Chapter 20: Functions
Algebra
4 topics
What this chapter covers
The 4 topics below make up Functions on the CAT. Click any topic to open its notes, examples and practice test.
Study material & tests
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Notes, worked examples and hint-guided practice for every topic.
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🎯 Topic tests
8 auto-graded questions per topic, pulled from the question bank.
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📝 Chapter test
25 fresh mixed-difficulty questions, timed, with full solutions.
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Formula Reference Sheet
This chapter
Definitions and tests
| Function rule | each x in domain → exactly one f(x) |
|---|---|
| Even function | f(−x) = f(x) (graph symmetric about y-axis) |
| Odd function | f(−x) = −f(x) (graph symmetric about origin) |
| Periodic function | f(x + T) = f(x) for least T > 0 |
| Composite function | (f∘g)(x) = f(g(x)) |
| Inverse condition | f(f⁻¹(x)) = x and f⁻¹(f(x)) = x |
CAT power-tools
| Domain of √(g(x)) | need g(x) ≥ 0 |
|---|---|
| Domain of 1/g(x) | need g(x) ≠ 0 |
| One-one (injective) test | f(a) = f(b) ⇒ a = b |
| Onto (surjective) test | range = co-domain |
| Inverse of linear f(x)=ax+b | f⁻¹(x) = (x − b)/a |
| Self-inverse / involution | f(f(x)) = x (e.g. f(x)=1/x, a−x) |
CAT reference
🖩 Graphing Calculator