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Insert Lesson Title Here Course 2 Identifying IV QUESTION What are the three ways to show inverse variation?

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3 ways to show inverse variations: Insert Lesson Title Here Course 2 Identifying IV * by a table * by an equation * by a graph

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Insert Lesson Title Here Course 2 Identifying IV QUESTION How can a table show inverse variation?

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Table Insert Lesson Title Here Course 2 Identifying IV - either x increases and y decreases, or x decreases and y increases (vary inversely) - the product of each x and corresponding y is the same x30155 y126

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Example of Indirect Variation: 1. As x increases (3, 12, 48), y decreases 8, 2, 1/3). 2. What is the constant of variation of the table above? 3 8 = k or k = 24 12 2 = k or k = 24 48 1/3 = k or k =24Note k stays constant. xy 38 481/3 122 Course 2 Identifying IV

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Do these tables show IV? Insert Lesson Title Here Course 2 Identifying IV x1½¼ y4816 x-202 y10 x4.530.5 y2318 x-24-12-8 y-½-1 ½ YES NOYES

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Insert Lesson Title Here Course 2 Identifying IV QUESTION How can an equation show inverse variation?

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Equation Insert Lesson Title Here Course 2 Identifying IV - written in the form: y = k/x - other possible form: xy = k - k = 0 Example: y = 4/x

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Do these equations show IV? Insert Lesson Title Here Course 2 Identifying IV y = 6x 2y = x y/8 = 1/x y = 3.4/x NO YES xy = -12 YES y = -4/x + 2 NO

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Insert Lesson Title Here Course 2 Identifying IV QUESTION How can a graph show inverse variation?

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Graph Insert Lesson Title Here Course 2 Identifying IV - curved line formed by connected points will NOT go through the origin - approaches the axes but never crosses them

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Do these graphs show IV? Insert Lesson Title Here Course 2 Identifying IV NO YES NO YES

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Insert Lesson Title Here Course 2 Identifying IV QUESTION What is the proportion for indirect or inverse variation?

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Proportion: Insert Lesson Title Here Course 2 Identifying IV 1. Arrange one pair as the numerator of one ratio and the denominator of the other. 2. Arrange the other pair in the same manner.

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Insert Lesson Title Here Course 2 Identifying IV VOCABULARYKIM inverse variation - one variable increases, other decreases - product of variables x and y is constant y = k/x

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Is this an inverse variation? Course 2 Identifying IV

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Finding and Using Inverse Functions: Lesson 50. LESSON OBJECTIVE: 1)Recognize and solve direct and joint variation problems. 2)Recognize and solve inverse.

Finding and Using Inverse Functions: Lesson 50. LESSON OBJECTIVE: 1)Recognize and solve direct and joint variation problems. 2)Recognize and solve inverse.

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