COLLEGE ALGEBRA
Name
Unit 3b Study Guide
Directions: Show all work and reasoning to receive full credit.
1) Accurately graph the following function by determining the following: f ( x) 
a) horizontal or oblique asymptote
3x 2  11x  4
2 x 2  5 x  12
b) write f in lowest terms
1
1
c) vertical asymptotes and holes
e) x- and y-intercepts
d) domain and range
f) additional points
2) Accurately graph the following function by determining the following: f ( x) 
a) horizontal or oblique asymptote
x3  x 2  12 x
x2  4
b) write f in lowest terms
1
1
c) vertical asymptotes and holes
e) x- and y-intercepts
d) domain and range
f) additional points
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 x3  4 x  6 x2
b) 2 x5  5x4  18x3  45x2
c)
12 x
 6x
4 x
6) Determine all of the complex zeros of the given polynomial functions (no decimal answers).
a) g ( x)  2 x2  x  5
b) h( x)  4 x4  22 x 2  42
c) f ( x)  3x 4  81x
7) Determine all of the real zeros of the polynomial function, and then use the real zeros to factor f over the real
numbers.
f ( x)  3x 4  x3  15x 2  x  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 x4  9 x3  21x 2  36 x  20
9) Use the given zeros to find the remaining zeros of the function. No decimal values.
f ( x)  3x4 19 x3  69 x2  99 x  26; zero: 2  3i
10) Find all zeros of the function and write the polynomial as a product of linear factors (no decimal values).
g ( x)  x4  2 x3  5x2  18x  36
11) Find a fourth degree polynomial in standard form that has the given zeros: 1, 3, 2  3i