https://file.aiquickdraw.com/mathbot/file/17302062333321ygp26f4.jpg

To determine which of the arrow diagrams represents an onto function, we must recall that an **onto function** (or surjective function) is one where every element in the target set \( Y \) has at least one element in the domain \( X \) that maps to it. This means every element in \( Y \) is covered by the mapping from \( X \).

Let's analyze each diagram:

### Diagram I
In Diagram I, the elements in set \( X = \{1, 2, 3\} \) are mapped to elements in set \( Y = \{a, b, c\} \). Checking the connections:
- \( 1 \rightarrow a \)
- \( 2 \rightarrow b \)
- \( 3 \rightarrow b \)

In this mapping:
- \( a \) has one pre-image (from 1),
- \( b \) has two pre-images (from 2 and 3),
- \( c \) has no pre-image.

Since \( c \) in \( Y \) is not mapped to by any element in \( X \), Diagram I is **not onto**.

### Diagram II
In Diagram II, \( X = \{1, 2, 3, 4\} \) and \( Y = \{a, b, c\} \). The mappings are as follows:
- \( 1 \rightarrow a \)
- \( 2 \rightarrow b \)
- \( 3 \rightarrow c \)
- \( 4 \rightarrow c \)

In this mapping:
- \( a \) has one pre-image (from 1),
- \( b \) has one pre-image (from 2),


Which of the following arrow diagrams below shows an onto function?

Determine which arrow diagram represents an onto function. Explore the concept of surjective functions and mappings between sets with detailed analysis of each diagram. Suitable for high school students in Grades 10-12.

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