Answer:
- domain: -5 < x ≤ 1
- range: -3 ≤ y ≤ 1
- is a function
Explanation:
The domain of a relation is the set of values of the independent variable for which the function is defined. It is the horizontal extent of the graph.
The range of a relation is the set of values the dependent variable may have. It is the vertical extent of the graph.
A relation is a function if there is only one output value for any given input value. That is, a vertical line can intersect the graph in at most one place.
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a)
domain
This graph extends from x > -5 to x = 1. The domain is ...
-5 < x ≤ 1 . . . . . . . (-5, 1] in interval notation
range
This graph extends from y = -3 to y = 1. The left side of the graph does not include the point (-5, 1), but the right side includes the point (1, 1). So y = 1 is one of the output values of the relation. The range is ...
-3 ≤ y ≤ 1 . . . . . . . . [-3, 1] in interval notation
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b)
No vertical line crosses the graph in more than one place, so the relation shown is a function.
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Additional comment
Sometimes a relation is given as a table or a list of ordered pairs. If there are no repeated x-values (inputs), the relation is a function. Repeated x-(input) values usually have different output values, so violate the requirement that a function have only one output for each input.