1. 6.3 – Square Root Functions and Inequalities
Day 1

2. Vocabulary:
Square Root Function – a function that contains the square root of a variable.
- A type of radical function.

4. Domain of Square Root Functions:
Domain: (What type of #’s can/cannot
be underneath a square root???)
• # CANNOT be negative, so…
the # (or expression) has to be > 0!

5. Range of Square Root Functions:
Range: (What type of #’s will result
from square rooting a #???)
• Answers WILL NOT be negative, so…
the y-values resulting from the
square root function have to be > 0!

6. Example 1:
Identify the domain and range of

7. Example 2:
Identify the domain and range of

9. Example 3:
Graph the function. State the domain and range.

10. Example 4:
Graph the function. State the domain and range.

11. Example 5:
Graph the function.
A. B.
C. D.

12. Ticket Out:
State the domain and range of the function. Hw – pg. 403, #13 – 16, 22 – 28 even
A. D: {x | x ≥ –1}; R: {y | y ≤ –4}
B. D: {x | x ≥ 1}; R: {y | y ≥ –4}
C. D: {x | x ≥ –1}; R: {y | y ≤ 4}
D. D: {x | x ≥ 1}; R: {y | y ≤ 4}

13. 6.3 – Square Root Functions and Inequalities
Day 2

14. Example 1:
When an object is spinning in a circular path of radius 2 meters with velocity v, in meters per second, the centripetal acceleration a, in meters per second squared, is directed toward the center of the circle. The velocity v and acceleration a of the object are related by the function

15. Example 1:
a. Graph the function in the domain {a|a ≥ 0}.

16. Example 1:
b. What would be the centripetal acceleration of an object spinning along the circular path with a velocity of 4 meters per second?

17. Square Root Inequalities
An inequality involving square roots.
Graph using same method as other inequalities.
- Solid or dashed line???
- Shade above or below??? (Test point.)
* From endpoint, shade straight up/down.

18. Example 2:
Graph

19. Example 3:
Graph
A. B.
C. D.

20. Ticket Out:
Graph Hw – pg. 403, #8, 29, 30, 32 – 38 even

21. 6.3 – Cube Root Functions
Day 3

22. Domain of Cube Root Functions:
Domain: (What type of #’s can/cannot
be underneath a cube root???)
• Any # can be put under a cube root!
Domain: All real numbers

23. Range of Cube Root Functions:
Range: (What type of #’s will result
from cube rooting a #???)
• Answers could be ANY #!
Range: all real numbers

24. Example 1:
Graph the function. State the domain and range. (Parent function for cubed roots.)

25. Example 2:
Graph the function. State the domain and range.

26. Example 3: (You try)
Graph the function. State the domain and range.

27. Example 4:
Graph the function. 𝑓 𝑥 ≤ 𝑥−1

28. Example 5: (You try)
Graph the function. 𝑓 𝑥 >−2 3 𝑥−3 −1

29. Ticket Out:
Graph the function.
𝑓 𝑥 >− 3 𝑥 +3
Hw – Worksheets