CORE_MATH • SHS 1Term 2WAEC / WASSCE SyllabusVIP Lesson
Relations, Functions & Graphs
Types of relations, domain, codomain, range, function notation f(x), composite functions, and drawing linear graphs from tables.
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Real-World Context & Relevance in Ghana
Ghana Water Company calculates monthly customer water bills as a function of cubic meters consumed using a linear billing tariff formula.
Key Syllabus Learning Objectives
- 1Distinguish between relations and functions using arrow diagrams and vertical line tests
- 2Identify domain, codomain, and range from given mappings
- 3Evaluate functions and composite functions f(g(x))
- 4Construct a table of values and plot straight-line graphs on Cartesian axes
1
Vertical Line Test
A graph represents a function if and only if no vertical line intersects the curve at more than one point. If a vertical line touches the graph twice, the same input has multiple outputs, so it is not a function.
- Straight lines (non-vertical) are functions.
- Parabolas y = ax² + bx + c are functions.
- Circles x² + y² = r² are NOT functions.
Core Takeaway:
Each domain element must map to one and only one codomain element.
WAEC / WASSCE Examiner Tips
- Always label your Cartesian axes clearly with variable names (x and y) and origin (0, 0).
- Use the exact scale stated in the examination question (e.g. 2 cm to 1 unit on both axes).
- Plot points with a sharp pencil using small crosses (×) or circled dots (⊙).
Common Candidate Pitfalls & Errors to Avoid
- Confusing codomain (all possible target elements) with range (actual mapped elements).
- Using an incorrect scale on axes, leading to immediate deduction of scale marks.
- Connecting plotted points with freehand curves instead of a straight ruler for linear functions.
Topic Mastery Checklist
- Can I determine if a relation is a function?
- Can I calculate f(-3) for f(x) = 2x² - 5x + 1?
- Can I find the range of f(x) given domain {0, 1, 2, 3}?
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10 WAEC-standard multiple choice questions with instant explanations.
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