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Understanding Square and Cube Root Functions: Transformations and Graphing Techniques

This guide covers the fundamental concepts of square root and cube root functions, including their parent functions, domains, and ranges. It explains how to apply transformations using the equations y = a√(x-h) + k and y = a3√(x-h) + k. The focus is on how to shift and stretch the graphs, with examples illustrating how to modify y-values and x-values through translations. Graphing techniques, including labeling parents and transformations, are emphasized, providing a comprehensive understanding of radical functions.

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Understanding Square and Cube Root Functions: Transformations and Graphing Techniques

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Presentation Transcript

  1. Section 6.5 Graph Square Root and Cube Root Functions

  2. Radical Functions • Review: • y = √x & y = 3√x • New: • y =a √(x-h) + k & y = a3 √(x – h) + k

  3. Parent Function: y = √x • Domain: x > 0 • Range: y > 0

  4. Parent Function: y = 3√x • Domain: all real numbers • Range: all real numbers

  5. y =a √(x-h) + k & y = a3√(x – h) + k Translations and Shifts • a & k change the y-value • Take the original y-value • a(y) + k • h changes the x-value • Take the original x-value • x + h

  6. EXs. • y = 2 √x + 2 • Change the y: • Double it and add 2 • y = -1 √(x – 1) – 3 • Change the y: • Take the opposite and subtract 3 • Change the x: • Add 1

  7. Points of Importance: y = √x Points of Importance: y = 3√x

  8. EX. y = 2 √(x – 1) + 3 • Now Plot!

  9. Now Graph…

  10. Ex. y = -33√(x + 7) - 6

  11. Note: • Label the parent and translation. • Make the parent graph be the dashed curve. • Show the table of values.

  12. Your Turn: • 449 • A:3,7,11,17,19,29,41,43 • B:6,10,16,32,44,47 • C:5,15,19,20,30,50

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