Question

Which relations are functions? Select Function or Not a function for each graph.

Answer 1

A function will not have any repeating x values...it can have repeating y values, just not the x ones. Plus, a function will pass the vertical line test.

1st graph....not a function
2nd graph ..thats a function
3rd graph...not a function
4th graph....thats a function

Answer 2

Answer: The graph (1) and (3) are not the graph of a function and only figure (2) and (4) shows the graph of a function.

Explanation:

A graph represents a graph of a function if the graph specifies the vertical line test.

Vertical line test states that the graph intersect each vertical line not more than one time. If the graph intersects any vertical line more that one time then it is not a graph of a function.

In figure (1) When we draw a vertical line on x = -3, then the curve intersects the line two times, therefore it is not a graph of a function.

In figure (3) When we draw a vertical line on x = 1, then the curve intersects the line two times, therefore it is not a graph of a function.

In figure (2) and (4) the curve and line will intersects all vertical line only one time, therefore figure (2) and (4) shows the graph of a function.