Question

state whether the following graph, table, coordinates, and mapping are functions.

Explanation:

For the Table:

Step1: Recall the definition of a function

A function is a relation where each input (x - value) has exactly one output (y - value).

Step2: Analyze the x - values in the table

In the given table, the x - value \(x = 0\) is paired with two different y - values (\(y=6\) and \(y = 8\)). Since there is an input (\(x = 0\)) that has more than one output, the relation represented by the table is not a function.

For the Graph (Circle):

Step1: Use the vertical line test

The vertical line test states that a graph represents a function if and only if no vertical line intersects the graph more than once.

Step2: Apply the vertical line test to the circle

For a circle, if we draw a vertical line (for example, the line \(x = 0\) or any vertical line that passes through the circle), it will intersect the circle at two points. So, the graph of the circle fails the vertical line test. Thus, the relation represented by the circle graph is not a function.

Answer:

(for the table): The relation in the table is not a function because \(x = 0\) has two different \(y\) - values (\(6\) and \(8\)).