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Mastering Algebra I: Key Concepts and Practice Problems

Enhance your understanding of Relations, Functions, Direct and Inverse Variation, Domain and Range with examples and solutions. Learn how to represent relations using ordered pairs, tables, graphs, and mappings. Practice finding zeros of functions graphically and algebraically.

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Mastering Algebra I: Key Concepts and Practice Problems

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  1. Review Unit 5 Algebra I

  2. Vocabulary • Relation – a set of ordered pairs • Function – a relation where the x does not repeat • Direct Variation – y varies directly with x. y = kx • Inverse Variation – y varies inversely with x. xy=k • Domain – x values • Range – y values • k – constant of variation

  3. Representing Relations • Ordered Pairs (3,6)(5,3)(3,-3) • TableGraph. . • Mapping. 3 6 5 3 -3

  4. Direct and Inverse Variation • When y varies directly with x, x = 4 and y = 12, find x when y = 20. • When y varies inversely with x, x = 8 and y = 3, find y when x = 48.

  5. Direct and Inverse Variation • When y varies directly with x, x = 4 and y = 12, find x when y = 96. y = kx 12 = k(4) 96 = 3x k = 3 x = 32 **Equation y = 3x • When y varies inversely with x, x = 8 and y = 3, find y when x = 48. xy = k 8(3) = k 48y = 24 k = 24 y = ½ **Equationxy = 24

  6. Zeros of a Function • Where the line crosses the x axis • Two ways to determine: • Graph in the calculator, look at the table and see where the y value is zero, the corresponding x value is the answer. • Set the f(x) or y = to zero, then solve the resulting equation for x.

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