Answer:
1) Domain: (-∞, 6]
Range: [-4, ∞)
2) Domain: (-∞, 2]
Range: (-∞, 6]
3) Domain: (-7, 5]
Range: [-6, 2)
4) Domain: [-2]
Range: (-∞, ∞)
Explanation:
Definitions
An open circle indicates the value is not included in the interval.
A closed circle indicates the value is included in the interval.
An arrow shows that the function continues indefinitely in that direction.
Interval notation
( or ) : Use parentheses to indicate that the endpoint is excluded.
[ or ] : Use square brackets to indicate that the endpoint is included.
Domain & Range
The domain is the set of all possible input values (x-values).
The range is the set of all possible output values (y-values).
Question 1
From inspection of the graph, the maximum x-value is x = 6.
There is a closed circle at one endpoint of the curve at (5, -4).
The arrow at the other endpoint indicates that the line continues indefinitely in that direction.
Therefore, the domain of the relation is restricted: (-∞, 6]
From inspection of the graph, the minimum y-value is y = -4.
This value is included in the range since there is a closed circle at (5, -4).
The arrow at the other endpoint indicates that the line continues indefinitely towards y = ∞.
Therefore, the range of the relation is restricted: [-4, ∞)
Question 2
From inspection of the graph, the maximum x-value is x = 2.
There is a closed circle at one endpoint of the curve at (-6, 6).
The arrow at the other endpoint indicates that the line continues indefinitely in that direction.
Therefore, the domain of the relation is restricted: (-∞, 2]
From inspection of the graph, the maximum y-value is y = 6.
This value is included in the range since there is a closed circle at (-6, 6).
The arrow at the other endpoint indicates that the line continues indefinitely towards y = -∞.
Therefore, the range of the relation is restricted: (-∞, 6]
Question 3
From inspection of the graph, the minimum x-value is x = -7 and the maximum x-value is x = 5.
There is an open circle at endpoint (-7, 2). Therefore, x = -7 is not included in the domain.
There is an closed circle at endpoint (5, -4). Therefore, x = 5 is included in the domain.
Therefore, the domain of the relation is restricted: (-7, 5]
From inspection of the graph, the minimum y-value is y = -6 and the maximum y-value is y = 2.
This maximum value is not included in the range since there is an open circle at (-7, 2).
Therefore, the range of the relation is restricted: [-6, 2)
Question 4
From inspection of the graph, the line is a vertical line at x = -2.
Therefore, the domain is restricted to x = -2: [-2]
There are arrows at both endpoints of the line, indicating that the line continues indefinitely in those directions.
Therefore, the range of the relation is unrestricted: (-∞, ∞)