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# 1.6 functions as rules and tables

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### 1.6 functions as rules and tables

1. 1. Represent Functionsas Rules and Tables<br />Section 1.6<br />P. 35-40<br />
2. 2. Learning goal: The student will learn to represent functions as rules and tables.<br />Understand what a function is<br />Understand where a function can be used<br />
3. 3. Key Vocabulary<br />A pairing of inputs and outputs such that each input is paired with exactly one output.<br />Function <br />Domain<br />Range<br />The input (numbers)The output ( 2nd set of #’s)<br />The student will learn to represent functions as rules and tables.<br />
4. 4. Key Vocabulary<br />Independent Variable<br />Dependent Variable<br />The input variable – the one you put into the RULE<br />The output variable – because its value “depends” on the value of the input variable.<br />The student will learn to represent functions as rules and tables.<br />
5. 5. 10<br />Input gallons<br />12<br />13<br />17<br />Output dollars<br />19.99<br />23.99<br />25.99<br />33.98<br />The domain is the set of inputs:<br />10, 12, 13,<br />and17.The<br /> range is the set of outputs:<br />19.99, 23.99, 25.99,and 33.98.<br />EXAMPLE 1<br />Identify the domain and range of a function<br />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.<br />ANSWER<br />
6. 6. for Example 1<br />GUIDED PRACTICE<br />1. Identify the domain and range of the function.<br />SOLUTION<br />The domain is the set of inputs:0, 1, 2, and 4The range is the set of outputs:1, 2, and 5<br />
7. 7. EXAMPLE 2<br />Identify a function<br />Tell whether the pairing is a function.<br />a.<br />The pairing is not a function because the input 0ispaired with both 2 and 3.<br />
8. 8. Output<br />Input<br />0<br />0<br />2<br />1<br />8<br />4<br />6<br />12<br />EXAMPLE 2<br />Identify a function<br />b.<br />The pairing is a function because each input is pairedwith exactly one output.<br />
9. 9. 36912<br />1221<br />2.<br />12<br />9<br />6<br />3<br />Input<br />1<br />2<br />2<br />1<br />Output<br />for Example 2<br />GUIDED PRACTICE<br />Tell whether the pairing is a function.<br />SOLUTION<br />The pairing is a function because each input is pairedwith exactly one output.<br />
10. 10. 3.<br />7<br />4<br />2<br />2<br />Input<br />3<br />2<br />1<br />0<br />Output<br />247<br />0123<br />for Example 2<br />GUIDED PRACTICE<br />Tell whether the pairing is a function.<br />SOLUTION<br />The pairing is not a function because each input is notpaired with exactly one output.<br />
11. 11. 2xis 0, 2, 5, 7, and 8.<br />The domain of the function y<br /> =<br />Make a table for the<br /> function, then identify the range<br />of the function.<br />x<br />2<br />5<br />0<br />7<br />8<br />y<br />7<br />8<br />=<br /> 2x<br />2<br />14<br />2<br />16<br />2<br />2<br />10<br />2<br />0<br />2<br />5<br />0<br />4<br /> =<br /> =<br /> =<br /> =<br /> =<br />EXAMPLE 3<br />Make a table for a function<br />SOLUTION<br />The range of the function is 0, 4, 10, 14, and 16.<br />
12. 12. Input<br />4<br />6<br />0<br />10<br />1<br />6<br />Output<br />12<br />8<br />2<br />3<br />and let y<br />Let x be the input, or independent variable,<br /> or dependent variable. Notice that each<br />be the output,<br />output is 2 more than the<br /> corresponding input.<br /> So, a <br />rule for the function isy<br /> 2.<br /> x <br /> =<br /> +<br />The student will learn to represent functions as rules and tables.<br />EXAMPLE 4<br />Write a rule for the function.<br />SOLUTION<br />
13. 13. You are buying concert tickets that cost \$15 each. You can buy up to 6 tickets. Write the amount (in dollars) you spend as a function of the number of tickets you buy.Identify the independent and dependent variables.Then identify the domain and the range of the function.<br />EXAMPLE 5<br />Write a function rule for a real-world situation<br />Concert Tickets<br />
14. 14. 15<br />n<br />A<br />=<br />EXAMPLE 5<br />Write a function rule for a real-world situation<br />SOLUTION<br />Write a verbal model. Then write a function rule. Let nrepresent the number of tickets purchased and Arepresent the amount spent (in dollars).<br />Amount spent(dollars)<br />Tickets purchased (tickets)<br />Cost per ticket (dollars/ticket)<br />•<br />=<br />So, the function rule is A =15n. The amount spent depends on the number of tickets bought, so nis the independent variable and Ais the dependent variable.<br />
15. 15. Number of tickets, n<br />0<br />1<br />3<br />2<br />6<br />5<br />4<br />75<br />60<br />90<br />Amount (dollars), A<br />15<br />45<br />30<br />0<br />EXAMPLE 5<br />Write a function rule for a real-world situation<br />Because you can buy up to 6 tickets, the domain of the function is 0, 1, 2, 3, 4, 5, and 6. Make a table to identify the range.<br />The range of the function is 0, 15, 30, 45, 60, 75, and 90.<br />
16. 16. for Examples 3,4 and 5<br />GUIDED PRACTICE<br />4. Make a table for the function y – x= 5 with domain 10, 12, 15, 18, and 29. Then identify the range of the function.<br />SOLUTION<br />The range of the function is .<br />
17. 17. Time (hours)<br />1<br />2<br />4<br />3<br />Pay (dollars)<br />16<br />32<br />24<br />8<br />for Examples 3,4 and 5<br />GUIDED PRACTICE<br />5. Write a rule for the function. Identify the domain and the range.<br />SOLUTION<br />Letx be the input ,or independent variable and let y be the output, or dependent variable.Notice that each output is 8 times more than corresponding input .So as a rule of function y = 8x;<br />domain 1, 2, 3 and 4;<br />range 8, 16, 24 and 32.<br />
18. 18. At Classzone.com<br />“Write a Function Rule Animation”<br />Check it out – go to chapter one<br />
19. 19. Assignment: P. 38 (#1-8 ,12 – 16, 20-21, 23) and review for quiz 1.4-1.5 on pg. 33<br />Quiz tomorrow 1.4-1.5<br />Learning goal: The student will learn to represent functions as rules and tables.<br />