COLLEGE ALGEBRA
Unit 3b Study Guide
Name
Directions: Show all work and reasoning to receive full credit.
1) Accurately graph the following function by determining the following: a) horizontal or oblique asymptote c) vertical asymptotes and holes e) x - and y -intercepts
b) write f in lowest terms d) domain and range f) additional points
2) Accurately graph the following function by determining the following: a) horizontal or oblique asymptote c) vertical asymptotes and holes e) x - and y -intercepts
b) write f in lowest terms d) domain and range f) additional points

3 x
2 
11 x

4
2 x
2 
5 x

12
 x
3  x
2 
12 x x
2 
4
1
1
1
1

3) While traveling in a car, the centrifugal force F a passenger experiences as the car drives in a circle varies jointly as the mass m of the passenger and the square of the speed v of the car. If a passenger experiences a force of 144 newtons when the car is moving at a speed of 40 kilometers per hour and the passenger has a mass of 100 kilograms, find the force a passenger experiences when the car is moving at 70 kilometers per hour and the passenger has a mass of 80 kilograms.
4) The time t in hours it takes a satellite to complete an orbit around the earth varies directly as the radius r of the orbit (from the center of the earth) and inversely as the orbital velocity v . If a satellite completes an orbit
730 miles above the earth in 10 hours at a velocity of 29,000 mph, how long would it take a satellite to complete an orbit if it is at 1200 miles above the earth at a velocity of 30,000 mph? (Use 3960 miles as the radius of the earth and round final answer to the nearest thousandths.)
5) Solve the following inequalities. a) 4 x
3 
4 x

6 x
2 b) 2 x
5 
5 x
4 
18 x
3 
45 x
2 c)
12 x
4
 x

6 x

6) Determine all of the complex zeros of the given polynomial functions (no decimal answers). a) g x

2 x
2 x 5 b) h x

4 x
4 
22 x
2 
42 c) f x

3 x
4 
81 x
7) Determine all of the real zeros of the polynomial function, and then use the real zeros to factor f over the real numbers.
( )

3 x
4  x
3 
15 x
2  
2
8) Find all of the complex zeros of the polynomial function and write the polynomial as a product of linear factors. f x

4 x
4 
9 x
3 
21 x
2 
36 x

20

9) Use the given zeros to find the remaining zeros of the function. No decimal values. f x

3 x
4 
19 x
3 
69 x
2 
99 x
  i
10) Find all zeros of the function and write the polynomial as a product of linear factors (no decimal values).
( )
 x
4 
2 x
3 
5 x
2 
18 x

36
11) Find a fourth degree polynomial in standard form that has the given zeros:

1, 3, 2

3 i