1. a. Given the graph of the function find the following.
i. Estimate
ii. Estimate x such that
8.1-31
 2g
( ) 9g x  

2. Give the domain and range of the following radical functions.
a.
8.1-52

3. 3
xy  xy 2 xy 2
Minimum point: Minimum point: Maximum point:
Domain: Domain: Domain:
Range: Range: Range:

4. 4
Minimum point: Minimum point: Minimum point:
Domain: Domain: Domain:
Range: Range: Range:
3 xy 2 xy 4 xy

5. Give the domain and range of the following radical functions.
a.
b.
c.
8.1-45
( ) 10h x x 
( ) 8f x x 
5)(  xxg

6. a. Given the function find the following.
i.
ii. Estimate numerically(table or graph) x such that
8.1-36
6)(  xxf
)40(f
5)( xf

7. 8.4
7

8. 8
Algebraically:
.ISOLATE a square root term on one side of the equation.
.Square BOTH sides
.Repeat 1 and 2 until no square root term remains.
.Solve the new equation. (either linear or quadratic)
.Check that the proposed solution satisfies the ORIGINAL
equation.

9. Graphically:
.Set the equation = 0
.Graph y1 = left side and y2 = right side (0)
.Find the intersection of your graph on the x-
axis.
These (this) are the only possible solutions.
No need to check.

10. Solve the following equations.
a. b.
8.4-110
12a  3 8 12m  

11. Solve the following equations.
a. b.
8.4-411
7 3 1a a   7 10 6x   

12. The period of a simple pendulum for a small amplitude is given
by the function
Where is the period in seconds and L is the length of the
pendulum in feet.
a. Find the period of a pendulum if its length is 1ft.
b. How long does a pendulum need to be if we want the period to
be 2.5 seconds?
8.4-212
( )T L
( ) 2
32
L
T L 

13. 8.5
13

14. Simplify the following, using the imaginary number i.
a. b. c.
8.5.114
4 50 25

15. For each complex number, name the real part and the imaginary
part.
a. b.
8.5-215
7 2i 8i

16. Add or subtract the following complex numbers.
a. b.
8.5-316
(7 4 ) (6 5 )i i   (2 8 ) (6 3 )i i  

17. Multiply the following complex numbers.
a. b. c.
8.5-417
5(2 6 )i 3 (6 4 )i i (4 7 )(2 9 )i i 

18. Write the complex conjugate of the following.
a. b. c.
8.5-518
3 7i 5 8i 2i

19. Multiply the following complex numbers by their conjugates.
a. b. c.
8.5-619
3 5i 4 6i 2i

20. Divide the following. Put all answers in the standard form of a
complex number.
a. b. c.
8.5-720
9 21
3
i 2 5
3 2
i
i


8 5
3
i
i


21. Solve the following equations. Give answers in the standard form
of a complex number.
a. b.
8.5-821
2
16m   2
3 20x x  

22. Solve the following equations. Give answers in the standard form
of a complex number.
c.
8.5-822
3 2
6 10 0t t t  