This document introduces radical functions. It covers evaluating radical functions, finding the domain of radical functions, graphing radical functions, performing operations on functions such as addition and multiplication, and function composition. Examples are provided to illustrate evaluating functions, finding domains, graphing, performing operations, and function composition.

1. INTRODUCTION TO
RADICAL FUNCTIONS
Lesson 6

2. Summary of Topics
• Evaluate Radical Functions
• Find the domain of Radical functions

3. Evaluate Radical
Function

4. Find the indicated function values of
the function 𝑓 𝑥 = 4𝑥 − 3
a. 𝑓 3
b. 𝑓 4
c. 𝑓(7)
d. 𝑓(0)

5. Find the indicated function values of
the function 𝑓 𝑥 = 3𝑥 + 8
a. 𝑓 −2
b. 𝑓 0
c. 𝑓(2)
d. 𝑓(4)

6. Graph of Radical
Function

7. Graph the function 𝑓 𝑥 = 𝑥 − 2
•Assign values of x.
•Evaluate the function.
•Plot the points.
•Draw the graph.

8. Graph the function g 𝑥 = 2𝑥 + 6
•Assign values of x.
•Evaluate the function.
•Plot the points.
•Draw the graph.

9. Find the Domain
of Radical
Function

10. Find the domain of each function
a. 𝑓 𝑥 = 𝑥 − 6
b. h 𝑥 = 4𝑥 + 8
c. g 𝑥 = 5𝑥 − 15

11. Find the domain of each function
a. 𝑓 𝑥 = 𝑥 − 10
b. h 𝑥 = 3𝑥 + 15
c. g 𝑥 = 9𝑥 − 18

12. Performing Function
Operations

13. Operation Definition
Addition
Subtraction
Multiplication
Division
ℎ 𝑥 = 𝑓 𝑥 + 𝑔 𝑥
ℎ 𝑥 = 𝑓 𝑥 − 𝑔 𝑥
ℎ 𝑥 = 𝑓 𝑥 ∙ 𝑔 𝑥
ℎ 𝑥 =
𝑓(𝑥)
𝑔(𝑥)

14. Example: 𝑓 𝑥 = 5𝑥; 𝑔 𝑥 = 𝑥 + 2
Evaluate the following operations:
1. 𝑓 𝑥 + 𝑔 𝑥
2. 𝑓 𝑥 − 𝑔 𝑥
3. 𝑓 𝑥 ∙ 𝑔 𝑥
4.
𝑓(𝑥)
𝑔(𝑥)

15. Example: 𝑓 𝑥 = 4𝑥 − 3; 𝑔 𝑥 = 𝑥 + 5
Evaluate the following operations:
1. 𝑓 𝑥 + 𝑔 𝑥
2. 𝑓 𝑥 − 𝑔 𝑥
3. 𝑓 𝑥 ∙ 𝑔 𝑥
4.
𝑓(𝑥)
𝑔(𝑥)

16. Example: 𝑓 𝑥 = 8𝑥 + 2𝑥; 𝑔 𝑥 = 5𝑥
Evaluate the following operations:
1. 𝑓 𝑥 + 𝑔 𝑥
2. 𝑓 𝑥 − 𝑔 𝑥
3. 𝑓 𝑥 ∙ 𝑔 𝑥
4.
𝑓(𝑥)
𝑔(𝑥)

17. Performing Function
Composition

18. Example: 𝑓 𝑥 = 3𝑥 + 2; 𝑔 𝑥 = 𝑥 − 5
Define the following functions:
1. 𝑓 ○ 𝑔 (𝑥)
2. 𝑔 ○ 𝑓 (𝑥)
3. 𝑓 ○ 𝑓 (𝑥)
4. 𝑔 ○ 𝑔 (𝑥)

19. Example: 𝑓 𝑥 = 4𝑥 − 9; 𝑔 𝑥 = 2𝑥
Define the following functions:
1. 𝑓 ○ 𝑔 (𝑥)
2. 𝑔 ○ 𝑓 (𝑥)
3. 𝑓 ○ 𝑓 (𝑥)
4. 𝑔 ○ 𝑔 (𝑥)