Intro to Functions

# Intro to Functions - Relation A relation is a set of...

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Relation A relation is a set of ordered pairs where the first components of the ordered pairs are the input values and the second components are the output values. Function A function is a relation that assigns to each input number EXACTLY ONE output number. Be careful. Not every relation is a function. A function has to fit the above definition to a tee. Domain The domain is the set of all input values to which the rule applies. These are called your independent variables . These are the values that correspond to the first components of the ordered pairs it is associated with. Range The range is the set of all output values. These are called your dependent variables . These are the values that correspond to the second components of the ordered pairs it is associated with.

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Example 1 : Determine if the given relation is function or not. Give its domain and range. {(1, 2), (1, -2), (2, 3), (3, 4)} Is this a function or not? We need to ask ourselves, does every first element (or input) correspond with EXACTLY ONE second element (or output)? In this case, the answer is no. The input value of 1 goes with two output values, 2 and -2. It only takes one input value to associate with more than one output value to be invalid as a function. So, this relation would not be an example of a function. Domain We need to find the set of all input values. In terms of ordered pairs, that correlates with the first component of each one. So, what do you get for the domain? If you got {1, 2, 3}, you are correct! Note that if any value repeats, we only need to list it one time. Range We need to find the set of all output values. In terms of ordered pairs, that correlates with the second component of each one. So, what do you get for the range? If you got {2, -2, 3, 4}, you are absolutely right! Example 2 : Determine if the given relation is function or not. Give its domain and range. {(5, 10), (10, 10), (15, 10)}
Is this a function or not? We need to ask ourselves, does every first element (or input) correspond with EXACTLY ONE second element (or output)? In this case, the answer is yes. 5 only goes with 10, 10 only goes with 10, and 15 only goes with 10. Note that a relation can still be a function if an output value associates with more than one input

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Intro to Functions - Relation A relation is a set of...

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