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Pre-Algebra 12-8 Inverse Variation Check 12-5 Homework

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Pre-Algebra 12-8 Inverse Variation Pre-Algebra HOMEWORK Page 637-638 #11-14 & 31-34

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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.

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Pre-Algebra 12-8 Inverse Variation Todays Learning Goal Assignment Learn to recognize inverse variation by graphing tables of data.

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Pre-Algebra 12-8 Inverse Variation 12-8 Inverse Variation Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

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Pre-Algebra 12-8 Inverse Variation Warm Up Find f(4), f(0), and f(3) for each quadratic function. 1. f(x) = x 2 + 4 2. f(x) = x 2 3. f(x) = 2x 2 x + 3 20, 4, 13 39, 3, 18 Pre-Algebra 12-8 Inverse Variation 1 4 4, 0, 9 4

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Pre-Algebra 12-8 Inverse Variation Problem of the Day Use the digits 18 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 14 56 7

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Pre-Algebra 12-8 Inverse Variation Vocabulary inverse variation

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Pre-Algebra 12-8 Inverse Variation 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. xy = 120xy = k kxkx y =y = 120 x y =y = INVERSE VARIATION WordsNumbersAlgebra

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Pre-Algebra 12-8 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. Additional Example 1A: Identify Inverse Variation Number of Students23468 Number of Cookies128643 2(12) = 24; 3(8) = 24; 4(6) = 24; 6(4) = 24; 8(3) = 24 xy = 24The product is always the same. The relationship is an inverse variation: y =. 24 x

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Pre-Algebra 12-8 Inverse Variation Tell whether the relationship is an inverse variation. A. Try This: Example 1A x00000 y23456 0(2) = 0; 0(3) = 0; 0(4) = 0; 0(5) = 0; 0(6) = 0 xy = 0 The relationship is an inverse variation: y =. 0 x The product is always the same.

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Pre-Algebra 12-8 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. Additional Example 1B: Identify Inverse Variation Number of Students1224364860 Time (min)1530456075 12(15) = 180; 24(30) = 720 The relationship is not an inverse variation. The product is not always the same.

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Pre-Algebra 12-8 Inverse Variation Tell whether the relationship is an inverse variation. B. Try This: Example 1B x24812 y42186 2(4) = 8; 2(6) = 12 The relationship is not an inverse variation. The product is not always the same.

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Pre-Algebra 12-8 Inverse Variation Additional Example 2A: Graphing Inverse Variations Graph the inverse variation function. A. f(x) = 4 x xy 4 2 1 1 2 4 1212 1212 2 4 8 8 4 2 1

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Pre-Algebra 12-8 Inverse Variation Try This: Example 2A xy 4 2 1 1 2 4 1212 1212 1 2 4 8 8 4 2 1 Graph the inverse variation function. A. f(x) = 4 x

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Pre-Algebra 12-8 Inverse Variation Graph the inverse variation function. B. f(x) = Additional Example 2B: Graphing Inverse Variations 1 x xy 3 2 1 1 2 3 1212 1212 1313 1212 1 2 2 1 1212 1313

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Pre-Algebra 12-8 Inverse Variation Try This: Example 2B Graph the inverse variation function. B. f(x) = 8 x xy 8 4 2 1 1 2 4 8 2 4 8 8 4 2 1

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Pre-Algebra 12-8 Inverse Variation 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/in 2. Additional Example 3: Application Volume of Gas by Pressure on Gas Pressure (lb/in 2 )5101520 Volume (in 3 )30015010075 You can see from the table that xy = 5(300) = 1500, so y =. 1500 x If the pressure on the gas is 30 lb/in 2, then the volume of the gas will be y = 1500 30 = 50 in 3.

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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 Students10202540 Cost per student201085 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.

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Pre-Algebra 12-8 Inverse Variation Tell whether each relationship is an inverse variation. 1. 2. Lesson Quiz: Part 1 no yes

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Pre-Algebra 12-8 Inverse Variation Lesson Quiz: Part 2 3. Graph the inverse variation function f(x) =. 1 4x4x