Mathematics 120 (Precalculus) Fall, 2006
Review: Examination II
York College (CUNY)
Jamaica, NY 11451
web page: http://www.york.cuny.edu/~malk
1. Given the functions below:
a. f(x) = x2 - 2x
b. f(x) = -x3 + x2
iv. f(x + 2)
v. f(a +3)
2. If f(x) = 2x -3 and g(x) = -x2 + 3
a. f(4) =
b. f(-2) =
c. g(-3) =
d. (g o f)(3) =
e. (f o g)(-5) =
f. (g o f)(x) =
g. (f o g)(x) =
h. Find functions f and g such that (f o g)(x) is given by (3x -3)5
3. Find the inverse of the following functions:
a. y = g(x) = -3x + 7
b. y = h(x) = x3 + 8
c. y = s(x) = -x2 + 4 (domain: x less than or equal to 0).
4. Compute the value of:
5. Draw a graph of y = h(x) = -x3
a. Draw y = h(x+3)
b. Draw y = h(x-3)
c. Draw y = -h(x)
d. Draw y = h(x) + 6
e. Draw y = h(x) - 4
f. Draw y = |h(x)|
g. y = 1(x+2/3)3 - 5
i. Graph y = 2|x-5|
j. Graph y = -3x3
6. a. Use long division to divide x3 - 5x2 - 11 by x + 2. What quotient and remainder do you get?
b. Use long division to divide x3 - 5x2 - 11x + 7 by x2 - x + 4. What quotient and remainder do you get?
7. Use synthetic division to check:
a. Is 2 a root of x4 - x3 - 6x2 - x + 6 = 0?
b. The quotient when x4 - x3 - 6x2 - x + 6 is divided by x - 4.
c. The remainder when x4 - x3 - 6x2 - x + 6 is divided by x +3.
d. Is x-3 a factor of x4 - x3 - 6x2 + 6.
8. i. Convert the following angles in degrees to radians
ii. Determine for each of the following angles in what quadrant the angle lies
9. i. Convert the following angles in radians to degrees.
ii. Determine for each of the following angles in what quadrant the angle lies.
10. Find the quadrant in which each of the angles above is located.
11. Find the reference angle R which is associated with each of the angles above.
a. sin 90°
b. cos 720º
c. sin 3¹/4
d. cos -210°
e. sin 23¹/3
f. cos -25¹/6
g. cos 225°
h. sin -330°