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FUN with Functions! Lesson Study Group B February 2012 Objectives • I will be able to use a function table to write an equation. • I will be able to use the equation to complete the missing values in the function table. Algebra and FUNCTIONS 1.5 Prior Knowledge Finding Patterns • Find a pattern between the yellow column and the blue column. 4 1 7 9 3 6 4 6 0 3 The pattern is subtract 3 Prior Knowledge Finding Patterns • Find a pattern between the yellow row and the blue row. The pattern is multiply by 3 3 5 0 9 12 9 15 0 27 36 Prior Knowledge Finding Patterns • Find a pattern between the yellow column and the blue column. 16 4 4 8 36 24 1 2 9 6 The pattern is divide by 4 Prior Knowledge Finding Patterns • Find a pattern between the yellow row and the blue row. The pattern is add 2 3 5 7 0 1 5 7 9 2 3 What is a Function? x 8 y +4 12 A function is a rule, that for every value of x (input) gives exactly one value of y (output). What is a Function? x 7 y +4 11 A function is a rule, that for every value of x (input) gives exactly one value of y (output). Functions In the incomplete equation + 5 = ___ is the input (x) + 5 is the rule x+5=y y=x+5 _____ is the output (y) What is a Function Table? x y 4a 8a a 36 a 24 1a 2a 9a 6a • A function table is a way of organizing values. • Now you can find a pattern between an x value and a y value to write an equation. Connecting a Function to its Table Let’s imagine this equation The input is a number going in. + 5 = ___ + 5 is the rule x (input) y (output) The output is the result of applying the rule ( + 5) Steps for Writing an Equation • Step 1: Find a pattern • Step 2: Identify the rule • Step 3: Write an equation by adding x and y to the rule. Writing an equation x y 5 0 9 12 15 0 27 36 The rule is… ·3 = ___ 3x = y y = 3x Writing an equation x y 7 9 3 6 4 6 0 3 The rule is… -3 = ___ y=x-3 Writing an equation x 5 7 0 1 y 7 9 2 3 The rule is… y=x+2 +2 = ___ Writing an equation x 25 35 10 5 y 5 7 2 1 The rule is… y=x÷5 x y 5 ÷ 5 = ___ Steps for Writing an Equation Steps to Completing a Function Table • Step 1: Find a pattern • Step 2: Identify the rule • Step 3: Write an equation by adding x and y to the rule. • Step 4: Use the x value to calculate the y value. Function Tables The rule is: x y + 5 = ___ x y 5 7 10 13 15 17 10 12 15 18 20 22 Function Tables The rule is: x y · 3 = ___ x y 6 4 5 7 3 10 18 12 15 21 9 30 Function Tables Equation x–6=y y=x-6 x y 18 10 20 9 16 6 12 4 14 3 10 0 Function Tables Equation x–4=y y=x-4 x 6 9 11 20 15 40 y 2 5 7 16 11 36 Function Tables Equation x÷4=y y=x÷4 x y 20 8 4 24 12 28 5 2 1 6 3 7 Function Tables Equation x ·6 = y y=x·6 x y 3 5 0 9 6 7 18 30 0 54 36 42 Function Tables x+9=y Equation y = x +9 x 2 22 13 8 7 0 y 11 31 22 17 16 9 Function Tables Equation x ÷8 = y y=x÷8 x y 32 24 16 88 56 48 4 3 2 11 7 6 CST Released Question x y 9 2 4 11 81 18 36 99 Which equation could have been used to create this function table? a) b) c) d) y=x+9 y=x–9 y = 9x x y= 9 Justify your answer Word Problem Number of Family Members 1 2 5 9 Total Cost for Tickets $17 $34 $85 Choose the number to complete the function table to find how much 9 tickets will cost. a) $8 b) $102 c) $136 d) $153 Justify your answer Which table represents values of x and y such that y = x + 7? A. B. x y 1 C. x y 8 2 9 4 10 3 11 x Y x y 9 2 4 11 6 1 2 9 D. Justify your answer Objectives • I will be able to use a function table to write an equation. • I will be able to use the equation to complete the missing values in the function table. Ticket Out the Door! QUIZ Complete quiz from today’s lesson with the following information: Rule Equation Explanation Complete function table You Rule! Create your own function table with the following information: Rule Equation Completed Table: must have an x and a y include at least 4 rows of numbers Write a real life situation to go with your table Guess My Rule! Partner B pulls a card Input Output Partner A Partner B Partner A pulls a card Input Output Partner A Partner B