To determine if a relation is a function, we check whether each input (first value in the pairs) maps to exactly one output (second value in the pairs). Let’s analyze the given relations.

Problem 3:

The relation is: $\{(1, -2), (2, 1), (3, 6), (4, 13), (5, 22)\}.$

• Inputs (x-values): $1, 2, 3, 4, 5$
• Outputs (y-values): $-2, 1, 6, 13, 22$

Each input corresponds to exactly one output. This relation is a function.

Problem 4:

The relation is: $\{(7, 4), (5, -1), (3, -8), (1, -5), (3, 6)\}.$

• Inputs (x-values): $7, 5, 3, 1, 3$
• Outputs (y-values): $4, -1, -8, -5, 6$

Here, the input $3$ corresponds to two different outputs ($-8$ and $6$). This relation is not a function, as an input maps to multiple outputs.

Would you like further clarification or details about functions?

Related Questions:

1. What is the definition of a function in mathematics?
2. Can a relation with repeating outputs still be a function?
3. How can a vertical line test be used to identify a function on a graph?
4. What are examples of real-world situations where functions are used?
5. How can domain and range be identified for a given relation?

Tip:

Always check the uniqueness of outputs for each input to determine if a relation is a function!