Question

7 decide if the following relations are functions or not
function not a function
x y
1 2
3 2
5 6
7 6
{(1, 2), (2, 3), (4, 4), (5, 6)}

Explanation:

Step1: Check relation 1 (mapping)

A function requires each input (x-value) to have exactly one output (y-value). Here, the input 4 maps to both 1 and 5, violating the function rule.

Step2: Check relation 2 (table)

Each x-value (1, 3, 5, 7) has exactly one corresponding y-value. No x-value repeats with different y-values, so it follows the function rule.

Step3: Check relation 3 (ordered pairs)

Each x-value (1, 2, 4, 5) appears exactly once with one y-value. No x-value has multiple outputs, so it follows the function rule.

Answer:

1. Mapping diagram: Not a Function
2. Table: Function
3. Set of ordered pairs: Function