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

13-1 Tables and Functions Warm Up Evaluate each expression for the given value of the variable. 1. 4x – 1 for x = y + 3 for y = 5 3. x + 2 for x = –6 4. 8y – 3 for y = – –1 1 2 __ –19

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

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

Vocabulary function input output

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

Additional Example 1: Writing Equations from Function Tables y x 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 = = 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.

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

Check It Out: Example y 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 = = 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.

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

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

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

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.

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 m t m is equal to 4 times t. Compare t and m. m = 4t Write an equation.

Substitute the t and m values in the table to check that they are solutions of the equation m = 4t. Look Back4 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 ?

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.

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 m t m is equal to 3 times t. Compare t and m. m = 3t Write an equation.

Substitute the t and m values in the table to check that they are solutions of the equation m = 3t. Look Back4 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 ?

Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

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. h = 2r, where h is the height and r is the radius y = 3x; y 75310x

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 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 Lesson Quiz for Student Response Systems