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Understanding Functions: Definition, Examples, and Domain/Range Identification

Learn about functions, including their definition, characteristics, and how to identify their domain and range. Explore examples and practice problems to enhance your understanding. Suitable for students and anyone interested in math.

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Understanding Functions: Definition, Examples, and Domain/Range Identification

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  1. Functions

  2. What is a function? • A function consists of: • A set called the domain containing numbers called inputs, and a set called the range containing numbers called outputs. • The inputs and outputs must be paired such that each input is paired with one and only one output. 1 2 3 4 0 1 2 3 1 2 3 4 0 1 2 This input output table is a function. This input output table is not a function.

  3. Let’s identify the domain and range. • The input-output table shows the cost of various amounts of regular unleaded gas from the same pump. Identify the domain and range of the function. The domain is the set of inputs: 10, 12, 13, 17. The range is the set of outputs: 19.99, 23.99, 25.99, 33.98.

  4. Let’s try another… • Identify the domain and range of the function.

  5. Important Note • A function may be represented by a mapping diagram. Notice that an output may be paired with more than one input, but no input is paired with more than one input. Input 1 2 3 4 Output 0 1 2

  6. Is this a function? Input 0 5 20 Output 2 3 4 5

  7. Is this a function?

  8. Is this a function?

  9. Is this a function?

  10. Any Questions? Lemme Kno’ Holla 

  11. Function Rules • A function may be represented using a rule that relates one variable to another. • The input variable is called the independent variable. • The output variable is called the dependent variable because its value depends on the value of the input variable. • Function rules typically give the dependent in terms of the independent variable. • In an equation like y=x+3, you know that y is the dependent variable.

  12. Writing Functions • The rule of the function: the output is 3 more than the input. • Equation: y=x+3

  13. Try One… • The domain of the function y=2x is 0, 2, 5, 7, and 8. Make a table for the function, then find the range of the function.

  14. How about this… • Write the rule for the function.

  15. How about a word problem… • You are buying concert tickets that cost $15 each. You can buy up to 6 tickets. Write the amount (in dollars) you spend as the function of the number of tickets you buy. Identify the independent and dependent variables. Then identify the domain and range of the function.

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