Answer:
Domain: (-∞, 1) ∪ (1, ∞)
Range: (-∞, -2) ∪ (2, ∞)
Yes, it's a function.
Step-by-step explanation:
Information
- 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.
Domain
The domain of a function is the set of all possible input values (x-values).
From inspection of the given graph:
- There is an open circle at (1, 2) and (1, -2).
- The arrows show that the x-values continue indefinitely towards -∞ and ∞.
Therefore, the domain is all values of x except x = 1:
- Interval notation: (-∞, 1) ∪ (1, ∞)
Range
The range of a function is the set of all possible output values (y-values).
From inspection of the given graph:
- There is an open circle at (1, 2) and (1, -2) so the range does not include any values of y between (and including) -2 and 2.
- The arrows show that the y-values continue indefinitely towards -∞ and ∞.
Therefore, the range is all values of y except between -2 and 2:
- Interval notation: (-∞, -2) ∪ (2, ∞)
Functions
A function is a special type of relationship where each input (x-value) is related to exactly one output (y-value).
From inspection of the graph, as the two points where x = 1 are not included, each value in the range (y-values) corresponds to exactly one value in the domain, and so it is a one-to-one function.
