A relation pairs values; a function assigns each x exactly one y.
★ Must-know
📌 An ordered-pair set is a function if every repeated domain value has the same corresponding output; it is not a function when one domain value is paired with different outputs.
📌 The vertical line test identifies a graph as a function when every vertical line intersects the graph at no more than one point; otherwise, the graph is not a function.
Further detail
1. Regarding relations and functions, which of the following statements are correct?
2. A function is a relation in which each input has a corresponding output. Which statements are correct?
3. Consider ordered-pair sets and their repeated domain values. Which statements are correct?
What is a relation in mathematics?
A set of ordered pairs (x, y).
Why is the set {(0,0), (-1,1), (1,1), (-2,4), (2,4)} a function?
Because no domain value repeats with different outputs.
When is an ordered-pair set considered a function?
When every repeated domain value has the same output.
What does the vertical line test show about a graph?
It shows the graph is a function if every vertical line intersects it at most once.
Relation vs Function
Function assigns one y per x, relation may not.
Vertical line test
Graph is a function if vertical line intersects once.
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