1. Name:__________ warm-up 6-3
Find the inverse of {(4, 3), (8, 0), (–5, 6)}.
Find the inverse of f(x) = x + 3.

2. Find the inverse of f(x) = 2x – 1.
Determine whether the pair of functions are inverse functions. Write yes or no. f(x) = x + 7 g(x) = x – 7
Determine whether the pair of functions are inverse functions. Write yes or no. f(x) = 3x + 4 g(x) = x – 4

3. Which of the following functions has an inverse that is also a function?
A. f(x) = x2 + 3x – 2
B. g(x) = x3 – 8
C. h(x) = x5 + x2 – 4x
D. k(x) = 2x2

5. Details of the Day Activities:
EQ: How do radical functions model real-world problems and their solutions?
How are expressions involving radicals and exponents related?
I will be able to…
Activities:
Warm-up
Review homework
Notes: Inverse Functions and Relations
Class work/ HW
Quiz 6-1 and 6-2 tomorrow
Vocabulary:
square root function
radical function
square root inequality
Graph and analyze square root functions. .
Graph square root inequalities.

6. 6-3 Square Root Functions and Inequalities

7. A Quick Review Find the inverse of {(4, 3), (8, 0), (–5, 6)}.
Find the inverse of f(x) = x + 3.

8. A Quick Review Find the inverse of f(x) = 2x – 1.
Determine whether the pair of functions are inverse functions. Write yes or no. f(x) = x + 7 g(x) = x – 7

9. A Quick Review
Which of the following functions has an inverse that is also a function?
A. f(x) = x2 + 3x – 2
B. g(x) = x3 – 8
C. h(x) = x5 + x2 – 4x
D. k(x) = 2x2

10. Notes and examples

11. Notes and examples

12. Notes and examples

13. Notes and examples

14. Notes and examples

15. Notes and examples

16. Notes and examples

17. Notes and examples
A. PHYSICS 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
Graph the function in the domain {a|a ≥ 0}.

18. Notes and examples
What would be the centripetal acceleration of an object spinning along the circular path with a velocity of 4 meters per second?
It appears from the graph that the acceleration would be 8 meters per second squared. Check this estimate
Original equation
Replace v with 4.
Square each side.
Divide each side by 2.

19. Notes and examples
A. GEOMETRY The volume V and surface area A of a soap bubble are related by the function Which is the graph of this function?
B. GEOMETRY The volume V and surface area A of a soap bubble are related by the function What would the surface area be if the volume was 3 cubic units?

20. Notes and examples
Graph

21. Notes and examples