10-1 Tables and Functions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

10-1 Tables and Functions Warm Up Evaluate each expression for the given value of the variable. 1. 4x – 1 for x = y + 3 for y = x + 2 for x = y – 3 for y =

10-1 Tables and Functions 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

10-1 Tables and Functions MA.6.A.3.6 Construct and analyze tables…and equations to describe linear functions…using both common language and algebraic notation. Also MA.6.A.3.2 Sunshine State Standards

10-1 Tables and Functions Vocabulary function input output

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.

10-1 Tables and Functions Additional Example 1: Writing Equations from Function Tables y 43210x 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 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.

10-1 Tables and Functions Check It Out: Example 1A y x 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 y = 3x y = 3(10) y = 30

10-1 Tables and Functions Check It Out: Example 1B y x 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 1 more than 2 times x y = 2x + 1 y = 2(15) + 1 = = 31

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

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

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

10-1 Tables and Functions Check It Out: Example 2B A large pie costs $2 more than a small pie. Write an equation for the function. Tell what each variable you use represents. ℓ = large pie’s cost s = small pie’s cost ℓ = 2 + s

10-1 Tables and Functions 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. Additional Example 3: Problem Solving Application

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

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 ?

10-1 Tables and Functions Check It Out: Example 3 The school band tracked the number of tickets sold and the total amount of money received. They sold each ticket for the same price. They received $60 for 20 tickets, $66 for 22 tickets, and $81 for 27 tickets. Write an equation for the function.

10-1 Tables and Functions m t m = 3t Let t be the number of tickets. Let m be the amount of money received. Check It Out: Example 3 continued