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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. 1. __. 2. Warm Up Evaluate each expression for the given value of the variable. 1. 4 x – 1 for x = 2 2. 7 y + 3 for y = 5 3. x + 2 for x = –6 4. 8 y – 3 for y = –2. 7. 38. –1. –19. Problem of the Day

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 1 __ 2 Warm Up Evaluate each expression for the given value of the variable. 1. 4x – 1 for x = 2 2. 7y + 3 for y = 5 3.x + 2 for x = –6 4. 8y – 3 for y = –2 7 38 –1 –19

  3. Problem of the Day These are rits: 24042, 383, and 4994. These are not rits: 39239, 28, and 5505. Which of these are rits: 39883, 4040, and 101? Why? 101 is a rit because it is the same forward and backward

  4. Learn to use data in a table to write an equation for a function and to use the equation to find a missing value.

  5. Vocabulary function input output

  6. A function is a rule that relates two quantities so that each input value corresponds exactly to one output value.

  7. x 3 4 5 6 7 10 y 13 16 19 22 25 Compare x and y to find a pattern. Use the pattern to write an equation. Substitute 10 for x. Use your function rule to find y when x = 10. Additional Example 1: Writing Equations from Function Tables 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. y is 3 times x plus 4. y = 3x + 4 y = 3(10) + 4 y = 30 + 4 = 34

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

  9. x 3 4 5 6 7 10 y 10 12 14 16 18 Compare x and y to find a pattern. Use the pattern to write an equation. Substitute 10 for x. Use your function rule to find y when x = 10. Check It Out: Example 1 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. y is 2 times x + 4. y = 2x + 4 y = 2(10) + 4 y = 20 + 4 = 24

  10. You can write equations for functions that are described in words.

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

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

  13. 1 Understand the Problem 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. The answer will be an equation that describes the relationship between the number of tickets sold and the money received.

  14. 2 Make a Plan 3 Solve t 20 22 27 m 80 88 108 Compare t and m. Write an equation. You can make a table to display the data. Let t be the number of tickets. Let m be the amount of money received. m is equal to 4 times t. m = 4t

  15. 4 Look Back ? ? ? 80= 4•20 88= 4•22 108= 4•27 ? ? ? 80= 80 88= 88 108= 108 Substitute the t and m values in the table to check that they are solutions of the equation m = 4t. m = 4t (20, 80)‏ m = 4t (22, 88)‏ m = 4t (27, 108)‏

  16. 1 Understand the Problem 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. The answer will be an equation that describes the relationship between the number of tickets sold and the money received.

  17. 2 Make a Plan 3 Solve t 15 21 30 m 45 63 90 Compare t and m. Write an equation. You can make a table to display the data. Let t be the number of tickets. Let m be the amount of money received. m is equal to 3 times t. m = 3t

  18. 4 Look Back ? ? ? 45= 3•15 63 = 3•21 90= 3•30 ? ? ? 45= 45 63= 63 90= 90 Substitute the t and m values in the table to check that they are solutions of the equation m = 3t. m = 3t (15, 45)‏ m = 3t (21, 63)‏ m = 3t (30, 90)‏

  19. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

  20. x 0 1 3 5 7 y 0 3 9 15 Lesson Quiz 1. Write an equation for a function that gives the values in the table below. Use the equation to find the value for y for the indicated value of x. 2. Write an equation for the function. Tell what each variable you use represents. The height of a round can is 2 times its radius. y = 3x; 21 h = 2r, where h is the height and r is the radius

  21. Lesson Quiz for Student Response Systems 1. Identify an equation for a function that gives the values in the table below. Then, use the equation to find the value for y for the indicated value of x. A. y = 4x + 8; 21 B. y = 7x – 7; 21 C. y = 4x + 8; 28 D. y = 7x – 7; 28

  22. Lesson Quiz for Student Response Systems 2. Identify an equation for the function. Tell what each variable you use represents. The width of a swimming pool is twice its depth. A. w = 2d, where d is the width and w is the depth B. , where w is the width and d is the depth C. w = 2d, where w is the width and d is the depth D. , where d is the width and w is the depth

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