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Identifying Functions
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A sequence of inputs and outputs paired together
A Relation A sequence of inputs and outputs paired together
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Input and output grouped in parentheses The input is listed first
Ordered Pairs Input and output grouped in parentheses The input is listed first The output is second ( Venus, 19), (Mars, 5), (Earth, 7), etc. If inputs and outputs are both numbers, we get the same ordered pairs we are used to using for graphs (1, 7), (2, 4), (3, 6), …
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A relation, where each input has only one output.
A Function A relation, where each input has only one output. Note: if inputs do not repeat, the relation is automatically a function. If inputs do repeat, then each repetition must match to the same output. (2, 7), (3, 4), (4, 7) is a function. (2, 7), (3, 4), (3, 7) is not a function since the input 3 maps to two outputs 4 and 7.
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A Function Not a Function
Vertical Line Test A vertical line passed over a function, will only cross the function at one point at a time. A Function Not a Function
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Domain and Range of a Relation
Domain is a list of allowed inputs Note this graph has inputs of x ≥ 1 In interval notation, this is [1, ∞ ) The bracket is “squared” since 1 is included Range is the resulting outputs The range is all real numbers In interval notation ( –∞, ∞)
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