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Algebra 2 Unit 9: Functional Relationships

Algebra 2 Unit 9: Functional Relationships. Topic: Functions & Their Inverses. Vocabulary. Inverse Relation A relation that “undoes” a function. The domain of a function is the range of its inverse; the range of a function is the domain of its inverse.

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Algebra 2 Unit 9: Functional Relationships

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  1. Algebra 2 Unit 9: Functional Relationships Topic: Functions & Their Inverses

  2. Vocabulary • Inverse Relation • A relation that “undoes” a function. • The domain of a function is the range of its inverse; the range of a function is the domain of its inverse. • The graphs of a function & its inverse are symmetric about the line y = x. • One-to-one Function • A function in which each range value is paired with one and only one domain value. • If a function, f is one-to-one, then it’s inverse is also a one-to-one function and is notated f-1.

  3. Function is one-to-one. Inverse will also be a function. Function is not one-to one. Inverse will not be a function. Determining whether a function is one-to-one • If a function passes the horizontal line test, it is a one-to-one function. • Any horizontal line must pass through the graph of a function once and only once.

  4. Finding the inverse of a function Replace f (x) with y, then switch x & y in the equation. Solve the resulting equation for y. Take the square root of both sides (remember there are two solutions). Subtract 2 from both sides. Multiply both sides by 2. The resulting relation is the inverse of f (x).

  5. Inverse Functions • Determine if the given function is one-to-one. If so, find its inverse & state its domain & range. The graph of the function does not pass the horizontal line test. It is not one-to-one, therefore its inverse is not a function (and we’re done with this problem!)

  6. Inverse Functions • Determine if the given function is one-to-one. If so, find its inverse & state its domain & range. The graph of the function does pass the horizontal line test. It is one-to-one, therefore its inverse is a function, and we must find it.

  7. Inverse Functions • Determine if the given function is one-to-one. If so, find its inverse & state its domain & range. Replace f (x) with y and switch x & y. Solve for y to find the inverse. Since we know this is a function, we must notate it properly (change y to f-1). The domain & range of f (x) is all real #s, thus the domain & range of f-1(x) is all real #s.

  8. Homework Quest: Functions & Their Inverses Due 5/7 (A-day) or 5/8 (B-day)

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