The image you uploaded shows a diagram representing a mapping $f: A \to B$ between two sets. There are two sets labeled $A$ and $B$, and the elements of set $A$ (on the left) are mapped to the elements of set $B$ (on the right). Based on the provided diagram, I can help analyze the domain and range.

Key components:

• Domain refers to the set of input values (elements from set $A$).
• Range refers to the set of output values (elements from set $B$) that are actually used in the mapping (not necessarily all elements of $B$).

To determine which of the provided options (A, B, C, D) gives the correct domain and range, let's break down the sets:

1. Domain is the entire set $A$, which appears to be $\{a, b, c\}$.
2. Range will be the set of elements in $B$ that are mapped to by elements of $A$. From the diagram, it seems like elements of $A$ are mapped to either $2$ or $3$, so the range is $\{2, 3\}$.

Now let's check the options:

• a. Domain = $\{a, b, c\}$, Range = $\{2, 3\}$ (this is the correct option based on the analysis)
• b. Domain = $\{a, b, c\}$, Range = $\{1, 4\}$ (incorrect range)
• c. Domain = $\{a, b, c\}$, Range = $\{1, 2, 3, 4\}$ (incorrect range)
• d. Domain = $\{1, 2, 3, 4\}$, Range = $\{2, 3\}$ (incorrect domain)

Conclusion:

The correct answer is Option A: Domain = $\{a, b, c\}$, Range = $\{2, 3\}$.

Would you like more details or have any other questions?

Here are 5 related questions to deepen understanding:

1. How do you determine the domain and range in a function diagram?
2. What is the difference between range and codomain in a mapping?
3. How can we verify if a mapping is a function?
4. What is an injective (one-to-one) function in the context of mappings?
5. How would the diagram change if an element in $A$ was mapped to multiple elements in $B$?

Tip: Always check if each element in the domain maps to exactly one element in the range to ensure it’s a valid function.