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7.5 Graphs Radical Functions

Learn how to graph the square root and cube root functions, along with general equations and transformations. Understand how to manipulate graph shapes and interpret domain and range.

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7.5 Graphs Radical Functions

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  1. 7.5 Graphs Radical Functions

  2. Graph of the Square Root Note: We cannot graph imaginary numbers on the coordinate plane. Therefore, the graph stops at x = 0.

  3. Graph of the Cube Root Note: Since the index number is odd, we can graph the function for all x values. Therefore, the domain is all reals.

  4. The General Equation The general form of the square root function is The cube root function is

  5. Add a positive positive number to x. Shift left h. Add a negative number to x. Add a positive number to the radical. Add a negative number to the radical. Shift right h. Up k. Down k.

  6. Add a positive positive number to x. Shift left h. Add a negative number to x. Add a positive number to the radical. Add a negative number to the radical. Shift right h. Up k. Down k.

  7. Changing a a is greater than 1 a is greater than 0 and less than 1. a is less than 0.

  8. Problems Describe how to obtain the graph of g from the graph of f. Shift left 5 units. Reflect in y = 0, shift down 10 units.

  9. Problems State the domain and range. x > -6, y > 0 x, y all real numbers

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