Answer:
Domain: (-∞, ∞)
Range: (-∞, ∞)
Step-by-step explanation:
A relation is any set of ordered pairs, which can be thought of as (input, output).
A function is a relation in which no two ordered pairs have the same first component (inputs or x values) and different second components (outputs or y values).
Any nonvertical line is the graph of a function. Thus, any linear equation of the form y = mx + b defines a function.
In the given graph, each domain element (first component) is distinct and corresponds to exactly one range element (second component).
A great way to determine whether a relation is a function is through the "Vertical Line Test." According to the vertical line test, the graph of an equation represents y as a function of x if and only if no vertical line intersects the graph more than once.
I drew vertical lines for each point on your graph to show how the vertical line test works. As you can see on the image, each vertical line goes through the graph only once (as represented by the green dots). This means that this line passes the vertical line test, and is, therefore, a function.
In terms of the domain and range, since it is a linear function, it does not have any domain constraints, that is why the domain is all x values.
The domain of a linear function can be written as:
Set notation for domain : {x | x ∈ R } "The domain is the set of all x such that x is an element of all real numbers."
Interval notation for domain: (- ∞, ∞).
Similarly, the range of a linear function is all y values. It can definitely go as high or as low without any constraints or limitations.
The range of a linear function can be written as:
Set notation for range: {y | y ∈ R } "The range is the set of all y such that y is an element of all real numbers."
Interval notation for range: (- ∞, ∞).
