The domain: -5 < x ≤ 1 and the range: -3 ≤ y ≤ 1 is a function. b)
No, the vertical line crosses the graph in more than one place, therefore, the relation shown is a function.
What is the domain and range of the function?
The domain of a function is defined as the set of all the possible input values that are valid for the given function.
The range of a function is defined as the set of all the possible output values that are valid for the given function.
The domain of a relation is the set of values of the independent variable for a defined function.
The domain is the horizontal extent of the graph.
The range of a relation is the set of values of the dependent variable for a defined function.
The range is the vertical extent of the graph.
The vertical line can intersect the graph in at most one place.
a)
This graph extends from x > -5 to x = 1.
The domain
-5 < x ≤ 1 ------ (-5, 1] in interval notation
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).
y = 1 is one of the output values of the relation.
The range
-3 ≤ y ≤ 1 . . . . . . . . [-3, 1] in interval notation
b)
No, the vertical line crosses the graph in more than one place, therefore, the relation shown is a function.
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