introduction to radical functions

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)