1. 7.5 Graphs Radical Functions

2. Graph of the Square Rootx y -1 i 1 4 2
Note: We cannot graph imaginary numbers on the coordinate plane. Therefore, the graph stops at x = 0.

3. Graph of the Cube Root x y -4 -1 1 4 1.59 -1.591 4
1.59
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