19. The absolute value equation of the graph is: y — | x - 0 | + 2 where (0,2) is the vertex.
Domain: (-∞, ∞)
Range: (-∞, 2]
A function is a relation in which no two ordered pairs have the same first component (inputs/x-values/domain) and different second components (outputs/y-values/range).
In determining whether a given relation is a function, we need to ask ourselves, does every first element (or input) correspond with EXACTLY ONE second element (or output)?
In the case of an absolute value function, its relation is a function because each input corresponds to exactly one output. To demonstrate, I performed a Vertical Line test to show why it is a function.
The Vertical Line Test (VLT) allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function. As the attached graph of the absolute value function, EACH vertical line drawn crosses the graph only once. This graph passes the VLT, making it a function.
20.)
The set of first components (x-coordinates) in the ordered pairs is the DOMAIN of the relation.
The set of second components (y-coordinates) is the RANGE of the relation.
Domain: {-2, -1, 0, 1}.
Range: {4, 3, 2, 1, 0}.
The given relation is NOT a function. As you can see from the given diagram, the input value of 2 corresponds to two output values: 4 and 0.
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