Grade 12 Math: Function Mapping Worksheet
This worksheet focuses on understanding and applying function mapping concepts, including domain, codomain, range, and types of mappings (one-to-one, onto, bijective).
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Grade 12 Math: Function Mapping
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Read each question carefully and provide your answers in the spaces provided. Show all your work for full credit.
1. Define the following terms in the context of function mapping:
a) Domain:
b) Codomain:
c) Range:
2. Which type of mapping ensures that each element in the codomain has at most one corresponding element in the domain?
Onto mapping
One-to-one mapping
Bijective mapping
Many-to-one mapping
3. A function f: A → B is surjective if:
Every element in A maps to a unique element in B.
Every element in B has at least one pre-image in A.
Every element in A has exactly one image in B.
The domain and codomain are identical.
4. Consider the function f: ℝ → ℝ defined by f(x) = x². Determine if this function is one-to-one, onto, or bijective. Justify your answer.
5. Let A = {1, 2, 3} and B = {a, b, c}. Define a bijective function from A to B and represent it using a mapping diagram.
Function definition:
Mapping Diagram:
6. A function that is both one-to-one and onto is called a function.
7. If the range of a function is equal to its codomain, the function is said to be .
8. All one-to-one functions are also onto functions.
True
False
9. The inverse of a function exists if and only if the function is bijective.
True
False