7.5 Graphs Radical Functions

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