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IB MYP 4-5 Maths-Mappings – Study Notes

IB MYP 4-5 Maths- Mappings- Study Notes - New Syllabus

IB MYP 4-5 Maths- Mappings – Study Notes

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  • Mappings

IB MYP 4-5 Maths- Mappings – Study Notes – All topics

Mappings

Mappings

A mapping shows how each element in one set (called the domain) is paired with an element in another set (called the codomain). Mappings are often represented using arrows or function notation.

Terms:

  • Domain: The set of input values.
  • Codomain: The set of possible output values.
  • Range: The actual set of outputs obtained after mapping.

Types of Mappings:

 

  • One-to-One Mapping: Each element in the domain maps to a unique element in the codomain.
  • Many-to-One Mapping: Two or more elements in the domain map to the same element in the codomain.
  • One-to-Many Mapping: One element in the domain maps to multiple elements in the codomain (this is NOT a function).

Important Points:

  • A mapping that is a function has only one output for each input.
  • Mappings can be shown as:
    • Arrow Diagrams
    • Tables
    • Graphs
    • Function Notation: \( f(x) \)

Example :

The mapping \( x \mapsto x + 2 \) for \( x \in \{1, 2, 3, 4\} \).

▶️ Answer/Explanation

For each input, add 2:

  • 1 → 3
  • 2 → 4
  • 3 → 5
  • 4 → 6

Arrow diagram: Each element has a unique output.

Example : 

The mapping \( x \mapsto x^2 \) for \( x \in \{-2, -1, 0, 1, 2\} \).

▶️ Answer/Explanation

Square each input:

  • -2 → 4
  • -1 → 1
  • 0 → 0
  • 1 → 1
  • 2 → 4

Here, multiple inputs map to the same output (e.g., -1 and 1 both map to 1).

Example : 

The mapping from x to {x + 1, x − 1} for \( x \in \{2, 3\} \).

▶️ Answer/Explanation

2 → {1, 3}
3 → {2, 4}

This is NOT a function because one input maps to multiple outputs.

Additional Notes for MYP Level:

1. Understand mappings as functions and non-functions:

A function is a mapping where every input value (from the domain) is assigned to exactly one output. If an input maps to two or more outputs, it is not a function.

Example: Mapping: \( x \mapsto x^2 \) for \( x = \{-2, -1, 0, 1\} \)
Outputs: {4, 1, 0, 1}. This is a function because each input has exactly one output.

Non-function Example: Mapping: \( x \mapsto \pm \sqrt{x} \) for \( x = \{4, 9\} \)
Here, 4 → {2, -2}, 9 → {3, -3}. One input gives multiple outputs, so it’s NOT a function.

2. Interpret mappings from arrow diagrams, tables, and graphs:

Mappings can be represented in different ways:

    • Arrow Diagram: Draw two sets (domain and codomain) and connect elements using arrows. Example: {1, 2, 3} → {3, 4, 5} using rule \( x \mapsto x + 2 \).
    • Table: List inputs and corresponding outputs in columns.

Example:

xf(x)
13
24
35

Graph: Plot ordered pairs on a coordinate plane. A straight line for linear mapping, a curve for quadratic.

3. Recognize the difference between domain, codomain, and range:

Domain: All possible input values for the mapping.
Codomain: The full set of potential outputs defined by the rule.
Range: The actual outputs produced for the given domain.

Example: For \( f(x) = x^2 \) where domain = {1, 2, 3}, Codomain could be all real numbers, but the Range = {1, 4, 9}.

4. Practice drawing arrow diagrams and writing function notation:

Function notation gives the rule clearly: \( f(x) = 2x + 3 \) means “input x is multiplied by 2 and then add 3.”

Example: For \( f(x) = 2x + 3 \), if x = 4, then f(4) = 2(4) + 3 = 11.

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