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

Question

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 inpu

Answer 1

To determine whether the relation is a function, we need to check if each input (x-value) corresponds to exactly one output (y-value).

From the points plotted in the graph:

• (-5, 1)
• (-2, 0)
• (-1, 3)
• (-1, -2)
• (0, 2)
• (5, 1)

We can see that the input x = -1 corresponds to two different outputs: y = 3 and y = -2. Since one input can have multiple outputs, this violates the definition of a function.

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