1 / 8

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.

nimrod
Download Presentation

Algebra 2 Unit 9: Functional Relationships

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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)

More Related