1. Radical Functions Essential Questions
How do we graph radical functions and inequalities?
How do we transform radical functions by changing parameters?
Holt McDougal Algebra 2
Holt Algebra 2

2. Recall that exponential and logarithmic functions are inverse functions. Quadratic and cubic functions have inverses as well. The graphs below show the inverses of the quadratic parent function and cubic parent function.

3. A radical function is a function whose rule is a radical expression
A radical function is a function whose rule is a radical expression. A square-root function is a radical function involving . The square-root parent function is The cube-root parent function is

5. Comparing Radical Graphs
Describe how to obtain the graph of g from the graph of f.
Vertical shift:
3 units up
Horizontal shift:
5 units to the left
Vertical shift:
4 units down
Horizontal shift:
1 units to the right
Vertical shift:
6 units up
Horizontal shift:
1 units to the left

6. Graphing Radical Functions
Graph the radical function and identify the domain and range. Up
4 times as fast
Domain:
Range:

7. Graphing Radical Functions
Graph the radical function and identify the domain and range. Up
Horizontal shift:
2 times as fast
3 units to the left
Domain:
Range:

8. Graphing Radical Functions
Graph the radical function and identify the domain and range.
3 times as fast
Horizontal shift:
2 units to the right
Domain:
Range:

9. Graphing Radical Functions
Graph the radical function and identify the domain and range.
opposite
2 times as fast
Horizontal shift:
1 unit to the left
Vertical shift:
2 units down
Domain:
Range:

10. Graphing Radical Functions
Graph the radical function and identify the domain and range.
Left
2 times as fast
Domain:
Range:

11. Graphing Radical Functions
Graph the radical function and identify the domain and range.
opposite
normal
Horizontal shift:
2 units to the right
Vertical shift:
1 unit up
Domain:
Range:

12. Lesson 7.1 Practice A