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To determine whether a graph of a relation is also a function, Shayla declares that the y-axis is a vertical line and counts the number of times that the graph intersects the y-axis. If the graph has exactly one y-intercept, Shayla concludes that the graph shows a function. In all other cases, she declares that it is not a function.

User Patrickzdb
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Answer: Shayla's method for determining whether a graph of a relation is a function is not completely accurate. While it is true that a function can only have one y-intercept, the converse is not necessarily true. A graph can have exactly one y-intercept and still not be a function.

For example, a vertical line has exactly one y-intercept, but it does not define a function because the same value of x can have multiple y-values.

It is also important to note that a graph can be a function even if it does not intersect the y-axis at all.

A more accurate way to determine whether a graph represents a function is to use the vertical line test. This test states that if a vertical line can be drawn through the graph such that it intersects the graph in more than one point, then the graph does not represent a function. If a vertical line can be drawn through the graph such that it intersects the graph in exactly one point, then the graph represents a function.

Explanation:

User Brandon Molyneaux
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