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12-8 Inverse Variation Check 12-5 Homework Pre-Algebra 12-8 Inverse Variation Pre-Algebra HOMEWORK Page 637-638 #11-14 & 31-34 Pre-Algebra 12-8 Inverse Variation Students will be able to solve sequences and represent functions by completing the following assignments. • • • • Learn to find terms in an arithmetic sequence. Learn to find terms in a geometric sequence. Learn to find patterns in sequences. Learn to represent functions with tables, graphs, or equations. • Learn to identify linear functions. • Learn to recognize inverse variation by graphing tables of data. Pre-Algebra 12-8 Inverse Variation Today’s Learning Goal Assignment Learn to recognize inverse variation by graphing tables of data. Pre-Algebra 12-8 12-8Inverse InverseVariation Variation Warm Up Problem of the Day Lesson Presentation Pre-Algebra Pre-Algebra 12-8 Inverse Variation Warm Up Find f(–4), f(0), and f(3) for each quadratic function. 1. f(x) = x2 + 4 20, 4, 13 9 2. f(x) = 1 x2 4, 0, 4 4 3. f(x) = 2x2 – x + 3 39, 3, 18 Pre-Algebra 12-8 Inverse Variation Problem of the Day Use the digits 1–8 to fill in 3 pairs of values in the table of a direct variation function. Use each digit exactly once. The 2 and 3 have already been used. 8 1 Pre-Algebra 56 4 7 12-8 Inverse Variation Vocabulary inverse variation Pre-Algebra 12-8 Inverse Variation INVERSE VARIATION Words An inverse variation is a relationship in which one variable quantity increases as another variable quantity decreases. The product of the variables is a constant. Pre-Algebra Numbers 120 y= x xy = 120 Algebra y= k x xy = k 12-8 Inverse Variation Additional Example 1A: Identify Inverse Variation Tell whether the relationship is an inverse variation. A. The table shows how 24 cookies can be divided equally among different numbers of students. Number of Students Number of Cookies 2 3 4 6 8 12 8 6 4 3 2(12) = 24; 3(8) = 24; 4(6) = 24; 6(4) = 24; 8(3) = 24 xy = 24 The product is always the same. The relationship is an inverse variation: y = 24 x . Pre-Algebra 12-8 Inverse Variation Try This: Example 1A Tell whether the relationship is an inverse variation. A. x 0 0 0 0 0 y 2 3 4 5 6 0(2) = 0; 0(3) = 0; 0(4) = 0; 0(5) = 0; 0(6) = 0 xy = 0 The product is always the same. The relationship is an inverse variation: y = x0 . Pre-Algebra 12-8 Inverse Variation Additional Example 1B: Identify Inverse Variation Tell whether each relationship is an inverse variation. B. The table shows the number of cookies that have been baked at different times. Number of Students 12 24 36 48 60 Time (min) 15 30 45 60 75 12(15) = 180; 24(30) = 720 The product is not always the same. The relationship is not an inverse variation. Pre-Algebra 12-8 Inverse Variation Try This: Example 1B Tell whether the relationship is an inverse variation. B. x y 2 4 4 2 8 1 2(4) = 8; 2(6) = 12 1 8 2 6 The product is not always the same. The relationship is not an inverse variation. Pre-Algebra 12-8 Inverse Variation Additional Example 2A: Graphing Inverse Variations Graph the inverse variation function. A. f(x) = 4 x y x –4 –1 –2 –2 –1 –4 – 1 2 1 2 8 1 4 2 2 1 4 Pre-Algebra –8 12-8 Inverse Variation Try This: Example 2A Graph the inverse variation function. A. f(x) = – 4 x x y –4 1 –2 2 –1 4 – 1 2 1 2 –8 1 –4 2 –2 –1 4 Pre-Algebra 8 12-8 Inverse Variation Additional Example 2B: Graphing Inverse Variations Graph the inverse variation function. x y B. f(x) = –1 x –3 1 –2 –1 1 – 2 1 2 1 2 3 Pre-Algebra 3 1 2 1 2 –2 –1 –1 2 –1 3 12-8 Inverse Variation Try This: Example 2B Graph the inverse variation function. B. f(x) = 8 x y x –8 –1 –4 –2 –2 –4 –1 –8 1 8 2 4 4 2 1 8 Pre-Algebra 12-8 Inverse Variation Additional Example 3: Application As the pressure on the gas in a balloon changes, the volume of the gas changes. Find the inverse variation function and use it to find the resulting volume when the pressure is 30 lb/in2. Volume of Gas by Pressure on Gas 5 10 15 20 Pressure (lb/in2) 300 150 100 75 Volume (in3) You can see from the table that xy = 5(300) = 1500, so y = 1500 . x If the pressure on the gas is 30 lb/in2, then the volume of the gas will be y = 1500 ÷ 30 = 50 in3. Pre-Algebra 12-8 Inverse Variation Try This: Example 3 An eighth grade class is renting a bus for a field trip. The more students participating, the less each student will have to pay. Find the inverse variation function, and use it to find the amount of money each student will have to pay if 50 students participate. Number of Students by Cost per Student 10 20 25 40 Students 20 10 8 5 Cost per student You can see from the table that xy = 10(20) = 200, so y = 200 . x If 50 students go on the field trip, the price per student will be y = 200 50 = $4. Pre-Algebra 12-8 Inverse Variation Lesson Quiz: Part 1 Tell whether each relationship is an inverse variation. 1. yes 2. no Pre-Algebra 12-8 Inverse Variation Lesson Quiz: Part 2 1 . 3. Graph the inverse variation function f(x) = 4x Pre-Algebra