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Each graph represents a relation. Determine if the relation is a function. Then find the domain and range.

Each graph represents a relation. Determine if the relation is a function. Then find-example-1
User Blackdad
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The relation is a function with a domain of (-6, 6] and a range of (-2, 2).

How to determine a relation that is a function?

If any vertical line crosses the graph at more than one point, the relation is not a function, and in this case, since the graph is a straight line, and one end is a shaded circle while the other end is an open circle, we can see that any vertical line will cross the graph at most once. Therefore, the relation is a function.

Domain: The domain of a function is the set of all x-values. Looking at the graph, it appears that all x-values are covered between -6 and 6. However, since the circle at (6, 2) is open, we need to exclude that point from the domain. So, the domain is (-6, 6] (all x-values from -6 to 6, including -6 but excluding 6).

Range: The range of a function is the set of all y-values. Similarly, it looks like all y-values are covered between -2 and 2. However, since the circle at (6, 2) is open, we need to exclude that point from the range. So, the range is (-2, 2) (all y-values from -2 to 2, excluding both -2 and 2).

User Titin
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