Question

The graph represents a relation where x represents the independent variable and y represents the dependent variable.

a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma 3, at negative 1 comma negative 2, at 0 comma 2, and at 5 comma 1

Is the relation a function? Explain.

No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.

Answer 1

A relation is a set of ordered pairs that represent a connection between two variables, where the first value of the pair is the independent variable, and the second value is the dependent variable.

A function is a specific type of relation where for each input value (independent variable), there is exactly one output value (dependent variable). This means that there cannot be two different outputs for the same input value in a function.

In the given graph, we can see that there are two points with the same x-coordinate, -1, but different y-coordinates, 3 and -2. Therefore, for the input value of -1, there are two different output values, violating the definition of a function.

Hence, the relation represented by the given graph is not a function.

Therefore the answer is: No, because for each input there is not exactly one output.