1 / 15

Radical Functions and Equations

Radical Functions and Equations. radical. index. radicand. L. Waihman 2002. A radical function is a function that has a variable in the radicand. You can apply the same transformations to the graphs of radical functions as you can to polynomial functions.

josephine
Download Presentation

Radical Functions and Equations

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. Radical Functions and Equations radical index radicand L. Waihman 2002

  2. A radical function is a function that has a variable in the radicand. You can apply the same transformations to the graphs of radical functions as you can to polynomial functions. Horizontal shift left one Vertical shift down three Vertical stretch two.

  3. Radical Parent functions As x, f(x) As x0+, f(x)0 As x, f(x) As x0+, f(x)0 As x, f(x) As x–, f(x)– Click on each graph above to link to interactive page!

  4. Transformations We apply the transformations on these functions in the same manner as we did with the polynomial functions. Horizontal shift right 3 Vertical shift up 2 Vertical stretch of 3 Domain: Domain: Domain: Range Range: Range:

  5. Applying the transformations Vertical stretch 3 Horizontal shift left 1 Vertical shift down 1 Domain: Range: As x , f(x) ; As x -1+, f(x) -1 Reflect @ x-axis Vertical shrink of ½ Horizontal shift right 2 Vertical shift up 4 As x , f(x) - ; As x 2+, f(x) 4 Domain: Range:

  6. Applying the transformations Vertical stretch of 3 Horizontal shift left 2 Vertical shift down 4 Domain: Range: As x, f(x) ; As x - , f(x) -  Reflect @ x-axis Vertical shrink of ½ Horizontal shift right 1 Vertical shift up 2 As x, f(x) - ; As x - , f(x) Domain: Range:

  7. To solve a radical equation that has only one variable in the radicand, isolate that term on one side of the equation. If the index is 2, then square both sides of the equation. Radical Equations Given: Isolate the radical. Square both sides. Simplify and set equal to zero. Factor. Solve. Be careful!The new equation you created when you Squared both sides might haveextraneoussolutions!

  8. Solving Radical Equations Check your solutions! • These solutions may not be solutions to the original equation. The graph below illustrates that the derived equation may be different from the original equation. √

  9. Try: Check: Check Try:

  10. More Solving Radical Equations • A radical equation may contain two radical expressions with an index of 2. • To solve these, rewrite the equation with one of the radicals isolated on one side of the equals sign. • Then, square both sides. • If a variable remains in a radicand, you must repeat the squaring process.

  11. More Solving Radical Equations Try: Isolate one radical on each side of equals sign. Square both sides. Collect like terms on each side of equals sign. Simplify. Check: Square both sides again.

  12. More Solving Radical Equations Try: Check: √

  13. Radical equations with indexes greaterthan 2 can be solved using similar techniques. After isolating the term containing the radical, raise each side of the equation to the power equal to the index of the radical. Check: √

  14. Bonus Questions! • One type of transformation was not covered in this PowerPoint. Identify it and give and example of an equation with this type of transformation and then sketch its graph to illustrate the transformation. Identify the domain and range as well. • Solve the equation: click

More Related