1 / 6

One-to-One Functions

One-to-One Functions. A function is one-to-one if no two distinct values in the domain correspond to the same value in the range. For example, the function f ( x ) = x 2 is not one-to-one since f ( - 3 ) = 9 and f ( 3 ) = 9.

jeremy-caldwell
Download Presentation

One-to-One Functions

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. One-to-One Functions A function is one-to-one if no two distinct values in the domain correspond to the same value in the range. For example, the function f (x) = x2 is not one-to-one since f (- 3)=9andf (3)=9. In other words, two distinct domain values, - 3and3,correspond to the same range value, 9.

  2. One-to-One Functions There is a horizontal line test associated with the definition. If it there exists a horizontal line that touches the graph of a function in more than one place, the function is not one-to-one. Otherwise, the function is one-to-one.

  3. 20 Now look at its graph. 18 16 14 12 10 8 6 4 2 0 -4 -3 -2 -1 1 2 3 4 (- 3, 9) (3, 9) One-to-One Functions To see why the horizontal line test works, look again at the function, f (x) = x2. Earlier, using the definition, it was found not to be one-to-one. You can see that there exists a horizontal line that touches the graph at more than one place, (- 3, 9) and (3, 9). It only takes one horizontal line touching the graph at more than one place to conclude the function is not one-to-one.

  4. Try: Graph and use the horizontal line test to determine whether each function is one-to-one. (a) f (x) = x3 – x – 2. One-to-One Functions It is not one-to-one.

  5. Try: Graph and use the horizontal line test to determine whether each function is one-to-one. (b) f (x) = x3 + x – 2. One-to-One Functions It is one-to-one.

  6. One-to-One Functions END OF PRESENTATION

More Related