1. 10-1 Tables and Functions Learn to use data in a table to write an equation for a function and to use the equation to find a missing value.

2. 10-1 Tables and Functions Vocabulary function input output

3. 10-1 Tables and Functions A function is a rule that relates two quantities so that each input value corresponds exactly to one output value.

4. 10-1 Tables and Functions Additional Example 1: Writing Equations from Function Tables 2522191613y 1076543x y is 3 times x plus 4. y = 3x + 4 Compare x and y to find a pattern. Use the pattern to write an equation. y = 3(10) + 4 Substitute 10 for x. y = 30 + 4 = 34 Use your function rule to find y when x = 10. Write an equation for a function that gives the values in the table. Use the equation to find the value of y for the indicated value of x.

5. 10-1 Tables and Functions When all the y-values are greater than the corresponding x-values, use addition and/or multiplication in your equation. Helpful Hint

6. 10-1 Tables and Functions Check It Out: Example 1 1816141210y 76543x y is 2 times x + 4. y = 2x + 4 Compare x and y to find a pattern. Use the pattern to write an equation. y = 2(10) + 4 Substitute 10 for x. y = 20 + 4 = 24 Use your function rule to find y when x = 10. Write an equation for a function that gives the values in the table. Use the equation to find the value of y for the indicated value of x.

7. 10-1 Tables and Functions You can write equations for functions that are described in words.

8. 10-1 Tables and Functions Additional Example 2: Translating Words into Math The height of a painting is 7 times its width. h = height of painting Choose variables for the equation. h = 7w Write an equation. Write an equation for the function. Tell what each variable you use represents. w = width of painting

9. 10-1 Tables and Functions Check It Out: Example 2 The height of a mirror is 4 times its width. h = height of mirror Choose variables for the equation. h = 4w Write an equation. Write an equation for the function. Tell what each variable you use represents. w = width of mirror

10. 10-1 Tables and Functions Additional Example 3: Problem Solving Application The school choir tracked the number of tickets sold and the total amount of money received. They sold each ticket for the same price. They received $80 for 20 tickets, $88 for 22 tickets, and $108 for 27 tickets. Write an equation for the function. 1 Understand the Problem The answer will be an equation that describes the relationship between the number of tickets sold and the money received.

11. 10-1 Tables and Functions You can make a table to display the data. 2 Make a Plan Solve 3 Let t be the number of tickets. Let m be the amount of money received. 1088880m 272220t m is equal to 4 times t. Compare t and m. m = 4t Write an equation.

12. 10-1 Tables and Functions Substitute the t and m values in the table to check that they are solutions of the equation m = 4t. Look Back 4 m = 4t (20, 80) 80 = 4 20 ? 80 = 80 ? m = 4t (22, 88) 88 = 4 22 ? 88 = 88 ? m = 4t (27, 108) 108 = 4 27 ? 108 = 108 ?

13. 10-1 Tables and Functions Check It Out: Example 3 The school theater tracked the number of tickets sold and the total amount of money received. They sold each ticket for the same price. They received $45 for 15 tickets, $63 for 21 tickets, and $90 for 30 tickets. Write an equation for the function. 1 Understand the Problem The answer will be an equation that describes the relationship between the number of tickets sold and the money received.

14. 10-1 Tables and Functions You can make a table to display the data. 2 Make a Plan Solve 3 Let t be the number of tickets. Let m be the amount of money received. 906345m 302115t m is equal to 3 times t. Compare t and m. m = 3t Write an equation.

15. 10-1 Tables and Functions Substitute the t and m values in the table to check that they are solutions of the equation m = 3t. Look Back 4 m = 3t (15, 45) 45 = 3 15 ? 45 = 45 ? m = 3t (21, 63) 63 = 3 21 ? 63 = 63 ? m = 3t (30, 90) 90 = 3 30 ? 90 = 90 ?