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Graphing Square Root Functions and Rationalizing the Denominator

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Presentation Transcript

  1. Chapter 10 Square Root Functions and Geometry

  2. 10.1Graphing Square Roots

  3. Model Graph of a Square Root • Use a x, y table to graph it

  4. The Graphs We Know

  5. Domain of a Square Root Function • Radicand cannot be negative • Set the radicand ≥ 0 • Solve for x

  6. Shifts in Square Root Graphs Vertical Shift: *Notice K is NOT under the square root *Move the graph up k units if positive *Move the graph down k units if negative

  7. Explain the Shift Move the graph 6 units down

  8. Shifts in Square Root Graphs Horizontal Shifts: Right h units: Left h units: Notice it is all under the square root sign

  9. Explain the shift of Five units to the left

  10. Compare the graph of • Under the x axis • Translate one unit to the left • Translate 3 units down

  11. 10.1 Extension Rationalizing the Denominator

  12. A radical is simplified when: • The radicand contains no perfect square factors. • A fraction cannot have a radical in the denominator. • Radicand cannot include a fraction.

  13. Rationalizing the denominator YOU CAN NOT HAVE A RADICAL IN THE DENOMINATOR!! To get rid of it multiply by the radical over itself

  14. Examples

  15. Example

  16. Example

  17. Example:

  18. Example:

  19. Conjugates

  20. Assignment:RPJ: Page 268 (1-7) allTB: Page 508 (1-9,11-13) all

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