Step-by-step explanation:
A relation is any set of ordered pairs, which can be thought of as (input, output).
A function is a relation in which no two ordered pairs have the same first component (x-values or input) and different second components (y-values or output).
First row:
Months (input) and Days (output) = not a function. The month of February has two corresponding outputs: Days of 28 and 29.
{(13, 33), (17, 25), (22, 22), (25, 17), (33, 17)} = this relation is a function. Each input value (x-coordinate) corresponds to exactly one output value (y-coordinate).
Plot of Distance (mi) vs. Time (h): the graph represents a function. Each input value (x-coordinate) corresponds to exactly one output value (y-coordinate).
Second row:
{(1, 2), (5, 2), (5, 4), (7, 6), (11, 6), (11, 8)}: this relation is not a function. The input value of 5 has two corresponding output values: 2 and 4. The same goes with the input value of 11, which has two output values of 6 and 8.
Table of Age (x) and Shoe Size (y): does not represent a function. The x = 15 has two corresponding y-values: 10 and 10.5.
Diagram of x and y (bottom-left corner): this relation represents a function. Each input value corresponds to exactly one output value.
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