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4.8 Functions and Relations
Goal: Decide whether a relation is a function and use function notation
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Definitions Relation - Any set of ordered pairs
Function -A type of relation where there is exactly one output for every input. For every x there is exactly one y.
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x y 1 2 6 7 x y 1 2 6 7 Not a Function Function
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y = 2x x-y chart mapping x y input output -2 -1 1 2 -4 -2 2 4 -4 -2 -2
1 2 -4 -2 2 4 -4 -2 -2 -1 1 2 2 4 Function
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Determine whether the equation is a function.
x y input output x y input output -2 -1 1 2 2 1 2 1 -2 -1 1 2 -2 -2 -1 -1 1 1 1 1 2 2 2 2 Function Not a Function
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Vertical Line Test - Functions
y y y y x x x x Function y y y y x x x x
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Vertical Line Test - Functions
y y y y x x x x Function Function y y y y x x x x
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Vertical Line Test - Functions
y y y y x x x x Function Function Not a Function y y y y x x x x
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Vertical Line Test - Functions
y y y y x x x x Function Function Function Not a Function y y y y x x x x
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Vertical Line Test - Functions
y y y y x x x x Function Function Function Not a Function y y y y x x x x Not a Function Function Not a Function Not a Function
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x y Tell whether the relation below is a function. input output 1) 3)
1 x 5 Function Not a Function 2 3 2) x y 4) input output -3 -1 1 2 3 -2 4 -1 Not a Function 5 Not a Function 6
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Function Notation
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Evaluate the following.
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Evaluate the function over the domain,
x = -1, x = 0, x = 2.
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Graph the linear function.
f(x) x -3 -2 -1 1 2 3 6 5 4 3 2 1 x
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