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.
Domain definition
Set of all possible x-values.
Range definition
Set of all possible y-values.
Evaluate f(x)
Substitute x into function; simplify.
Operation: (f+g)(x)
Sum of f(x) and g(x).
Composition: (f∘g)(x)
Apply g to x, then f to g(x).
Test your knowledge with 10 questions on Functions and Operations.
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?
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