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Algebraic Test for One-to-One Functions: Examples and Calculator Instructions

Learn how to determine if a function is one-to-one algebraically, find inverses, use a calculator for graphs, and restrict domains. Includes step-by-step examples and calculator instructions.

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Algebraic Test for One-to-One Functions: Examples and Calculator Instructions

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  1. 1.6B Algebraic Test for One to One Functions • If f(a) = f(b) and a=b then the function is one- to- one. (like # 48-58) • Example: f(x)= + 1 Is f(x) one- to- one? • Example: f(x) = x² + 2 Is f(x) one -to -one?

  2. Draw inverse feature in Calculator • Put original in y= • 2nd, PRGM, 8:DrawInv, “VARS” → Y-Vars., 1:Function, choose original equation (Y₁ etc.), enter • 2nd, “mode”, 2nd, “PRGM”, 1:ClrDraw, enter,done

  3. Examples • #59. f(x)=2x – 3 Find inverse algebraically. Use Calculator to graph f(x) and together. Describe the relationship.

  4. More Examples • #69. f(x)= (x- 2)² Restrict the domain so f(x) is one- to- one and has a true inverse function. Find the inverse of f(x) algebraically. State domain & range of .

  5. More examples • # 81-87 odd. • 81. (0) • 83. (f ○ g)(2) • 85. (g(0)) • 87. (g ○ )(2)

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