1. Functions

2. What is a function? A function consists of: A function consists of: A set called the domain containing numbers called inputs, and a set called the range containing numbers called outputs. 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. The inputs and outputs must be paired such that each input is paired with one and only one output. 12341234 12341234 01230123 01230123 12341234 12341234 012012 012012 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 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. Input (gallons) 10121317 Output (dollars) 19.9923.9925.9933.98 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. Identify the domain and range of the function. Input0124 Output5221

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. 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 Input 1 2 3 4 Output 0 1 2 Output 0 1 2

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

7. Is this a function? InputOutput 00 12 48 612

8. Is this a function? InputOutput 31 62 92 121

9. Is this a function? InputOutput 20 21 42 73

10. Any Questions? Lemme Kno’ Holla Holla

11. Function Rules A function may be represented using a rule that relates one variable to another. A function may be represented using a rule that relates one variable to another. The input variable is called the independent variable. 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. 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. 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. 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. The rule of the function: the output is 3 more than the input. Equation: y=x+3 Equation: y=x+3 Input, x01234 Output, y 34567

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. 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. x02578 y=2x2(0)=02(2)=42(5)=102(7)=142(8)=16

14. How about this… Write the rule for the function. Write the rule for the function. Input014610 Output236812

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. 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.