Review: Examination II
Prepared by:
Joseph Malkevitch
Department of Mathematics
York College (CUNY)
Jamaica, New York 11451
email:
malkevitch@york.cuny.edu
web page:
http://york.cuny.edu/~malk/
1. Given the functions below:
a. f(x) = x2 - 2x b. f(x) = -x3 + x2
Compute:
i. f(-2)
ii. f(-3)
iii. f(1/2)
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:
a.
b.
c.
d.
e.
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. Perform the indicated calculations
a. (3+2i) - (4 + -3i) =
b. (3 + i)/(5-3i) =
c. (2 -3i) (-2 -5i) =
d. (i)((i -4) =
e. i39 =
f. -i45 =
7. Sketch a graph of the following, which shows (if any) x intercepts, y-intercept, vertical and horizontal asymptotes, and behavior for large and small values of x.
a.
b.
c.
d.
e.
8. i. Convert the following angles in degrees to radians
ii. Determine for each of the following angles (given in degrees) in what quadrant the angle lies
a. 360
b. 780
c. -210
d. 135
e. -225
f. -18
g. +10
9. i. Convert the following angles in radians to degrees.
a. 2¹
b. -¹/6
c. 5¹/3
d. -7¹/4
e. 6
ii. Determine for each of the following angles (given in radians) in what quadrant the angle lies.
a. -6¹
b. 3¹/4
c. -5¹/2
d. 19¹/6
e. 7¹/3
f. -39¹/4
g. -18
h. 10
10. Find the reference angle (in radians) which is associate with each of the following angles:
a. -6¹
b. 3¹/4
c. -5¹/2
d. 19¹/6
e. 7¹/3
f. -39¹/4
11. Find the reference angle R (in degrees) which is associated with each of the following angles:
a. 210
b. -330
c. -210
d. 135
e. -225
f. 120
g. -240
12. Compute:
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°
13. Draw graphs of the following by completing the square:
a. y = x2 - 4x + 3
b. y = 2x2 - 12x + 3
c. y = -x2 - 4x - 3
d. y = -4x2 + 8x + 3
14. Solve the following inequalites:
a. x2 - 4x > 0
b. -x2 - 4x > 0
c. x2 - 6x + 8 < 0
d. x2 - 6x + 9 > 0
e. -4 x2 - 4x + 3 > 0