1. 5.3 Graphing Radical Functions

2. Radical Functions
A radical function contains a radical expression with the independent variable in the radicand.
When the radical is a square root, the function is called a square root function.
When the radical is a cube root, the function is called a cube root function.

3. Square Root Functions
The radicand of a square root must be nonnegative.
Domain:
Range:
Domain:
Range: h

4. Cube Root Functions
The domain and range of cube root functions are all real numbers.
Domain: all real numbers
Range: all real numbers
Domain: all real numbers
Range:
all real numbers h

5. Example 1: Solution: 1. Make a table of values 2. Sketch the graph4 8 12 16 y 1
1.4
1.73 2
2. Sketch the graph
3. Domain and Range

6. Transformation
You can transform graphs of radical functions in the same way you transformed graphs of functions previously.
Transformation
f(x) notation
Example
Horizontal Translation
- shifts graph left/right
f(x – h)
Vertical Translation
- shifts graph up/down
f(x) + k
f(-x)
-f(x)
Reflection
- graph flips over x or y axis
Horizontal Stretch/Shrink
graph stretches away from or shrinks toward y axis
f(ax)
Vertical Stretch/Shrink
graph stretches away from or shrinks toward x axis
a • f(x)

7. Example 2:
Solution:
h = 3: shift three units right
k = 4: shift four units up

8. Example 3: Solution Step 1 Understand the Problem
Step 3 Solve the Problem
Step 4 Look Back
Step 2 Make a Plan

9. :D
Example 4:
Solution:

10. Example 5:
Solution
Step 2 Graph both radical functions.
Step 1 Solve for y.
The vertex is (0,0) and the parabola opens right.

11. Example 6:
Solution
Step 1 Solve for y
Step Graph both radical functions.