Question: Identifying functions from relations Relation 1 - Domain: \( b, t, y, u, z \) - Range:…

Identifying functions from relations

Relation 1

• Domain: \( b, t, y, u, z \)
• Range: \( -4, 2 \)

Relation 2

• Domain: \( z, b, f, u \)
• Range: \( b, f, z \)

Relation 3

• Domain: \( s, c, a, v \)
• Range: \( \text{lake}, \text{pencil} \)

Relation 4

• Domain: \( -8, -4, -2, -1, 6 \)
• Range: \( -9, 5, -8, 4, -9 \)

Function or Not a function

• Relation 1: Not a function
• Relation 2: Function
• Relation 3: Function
• Relation 4: Not a function

Solution

To determine if each relation is a function, we need to check if every element in the domain is mapped to exactly one element in the range. Relation 1: - Domain: \( b, t, y, u, z \) - Range: \( -4, 2 \) - Elements \( b, t, y, u \) all map to \(-4\). - Element \( z \) maps to \(2\). All elements in the domain map to exactly one element in the range, so this is a function. Relation 2: - Domain: \( z, b, f, u \) - Range: \( b, f, z \) - Element \( z \) maps to \(b\). - Element \( b \) maps to \(f\). - Element \( f \) maps to \(f\). - Element \( u \) maps to \(z\). All elements in the domain map to exactly one element in the range, so this is a function. Relation 3: - Domain: \( s, c, a, v \) - Range: \( \text{lake}, \text{pencil} \) - Elements \( s, c, a \) all map to \(\text{lake}\). - Element \( v \) maps to \(\text{pencil}\). All elements in the domain map to exactly one element in the range, so this is a function. Relation 4: - Domain: \( -8, -4, -2, -1, 6 \) - Range: \( -9, 5, -8, 4 \) - Element \(-8\) maps to \(-9\). - Element \(-4\) maps to \(5\). - Element \(-2\) maps to \(-8\). - Element \(-1\) maps to \(4\). - Element \(6\) maps to \(-9\). All elements in the domain map to exactly one element in the range, so this is a function. Final Answers: - Relation 1: Function - Relation 2: Function - Relation 3: Function - Relation 4: Function