1

a. Given the graph of the function find the following.

i. Estimate

ii. Estimate x such that

8.1-3

2g

( ) 9g x

2

Give the domain and range of the following radical functions.a.

8.1-5

3

xy xy 2 xy 2

Minimum point: Minimum point: Maximum point:Domain: Domain: Domain:Range: Range: Range:

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.

8.1-4

( ) 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

8.1-3

6)( xxf)40(f

5)( xf

7

8.4

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.

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.

8.4-1

12a 3 8 12m

11

Solve the following equations.

a. b.

8.4-4

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?

8.4-2

( )T L( ) 2

32

LT L

13

8.5

14

Simplify the following, using the imaginary number i.

a. b. c.

8.5.1

4 50 25

15

For each complex number, name the real part and the imaginary part.

a. b.

8.5-2

7 2i 8i

16

Add or subtract the following complex numbers.

a. b.

8.5-3

(7 4 ) (6 5 )i i (2 8 ) (6 3 )i i

17

Multiply the following complex numbers.

a. b. c.

8.5-4

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.

8.5-5

3 7i 5 8i 2i

19

Multiply the following complex numbers by their conjugates.

a. b. c.

8.5-6

3 5i 4 6i 2i

20

Divide the following. Put all answers in the standard form of a complex number.

a. b. c.

8.5-7

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.

8.5-8

2 16m 2 3 20x x

22

Solve the following equations. Give answers in the standard form of a complex number.

c.

8.5-8

3 26 10 0t t t