Is the following relation graphed below a function? Explain? Think about what open and closed circles mean

Given:

The graph of a relation.

To find:

Whether the given relation in the graph is a function or not.

Solution:

First we need to understand the meaning of open circles and closed circles.

Open circle: It is a unfilled circle, it means, that value is not included in the solution set.

Close circle: It is a completely filled circle, it means, that value is included in the solution set.

A relation is a function if their exist a unique y-value (output value) for each x-value (input value).

The graph of a relation is a function, if the graph intersect each vertical line at most once. It is known as vertical line test.

For the vertical lines x=-1 and x=1, the graph has only one close circle and all other vertical line intersect the graph at most once.

Since the graph passes the vertical line test, therefore it represents a function.

5y

step-by-step explanation:

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.