Question

for each relation, decide whether or not it is a function. part 1 of 2 relation 1 {(9, 7), (9, -7), (9, 2), (9, 9)} ∘ function ∘ not a function part 2 of 2 relation 2 {(g, -5), (v, -4), (f, -9), (w, 2)} ∘ function ∘ not a function

Explanation:

Step1: Recall the definition of a function

A relation is a function if each input (first element of the ordered pair) has exactly one output (second element of the ordered pair). In other words, no two ordered pairs in the relation can have the same first element with different second elements.

Step2: Analyze Relation 1

Relation 1 is \(\{(9, 7), (9, -7), (9, 2), (9, 9)\}\). Here, the input \(9\) is associated with multiple outputs: \(7\), \(-7\), \(2\), and \(9\). Since a single input has more than one output, this relation does not satisfy the definition of a function.

Step3: Analyze Relation 2

Relation 2 is \(\{(g, -5), (v, -4), (f, -9), (w, 2)\}\). Each input (\(g\), \(v\), \(f\), \(w\)) is associated with exactly one output (\(-5\), \(-4\), \(-9\), \(2\)) respectively. There are no repeated inputs with different outputs, so this relation satisfies the definition of a function.

Answer:

Part 1 of 2: Not a function
Part 2 of 2: Function