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Graphing Square Root Functions and Rationalizing the Denominator

Learn how to graph square root functions and rationalize the denominator in this chapter. Explore vertical and horizontal shifts in square root graphs and practice using conjugates in rationalizing.

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Graphing Square Root Functions and Rationalizing the Denominator

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  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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