The relationship classification in the figure are presented as follows;
{(0, -4) (2, 7) (4, -4) (1, 9) (3, 7)} True
Graph of x³ + y³ - 3·x·y = 0 False
Relations in the Set False
Relation in table y = 2·x + 3 True
The analysis of the relationships are as follows;
The set of ordered pairs {(0, -4), (2, 7) (4, -4) (1, 9) (3, 7)} is a function. Each input (x-value) maps onto exactly one output (y-value)
The relationship in the graph is not a function as it does not pass the vertical line test, that is if a vertical line is drawn in the graph between x = 0 and x = 1.5, intersects the graph twice, which indicates that one x-value maps onto two y-values
The relationship in the set of inputs and outputs is not a function as the input element 2 maps onto two output elements 20 and 40, which disputes the definition of a function
The relationship represented by the linear equation y = 2·x + 3 is a function as each x-value maps onto one y-value