Review: Examination II
prepared by:
Joseph Malkevitch
Mathematics Department
York College (CUNY)
Jamaica, NY 11451
email: joeyc@cunyvm.cuny.edu
web page: http://www.york.cuny.edu/~malk
1. Given the functions below:
a. f(x) = x2 - x b. f(x) = -x3 + x2
Compute:
i. f(-2)
ii. f(-3)
iii. f(1/2)
iv. f(x + 1)
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) + 7
e. Draw y = h(x) - 3
f. Draw y = |h(x)|
g. Graph y = 2|x-5|
h. Graph y = -3x3
6. What are the potential rational roots of the following polynomial equations?
a. x3 -4x + 3 = 0
b. x4 - x3 - 6x2 - x + 6 = 0
c. 3x3 - 5x2 - 5 = 0
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. Sketch a graph of the following:
(Show where the graph cuts the x-axis, y-axis (if it does), vertical asymptotes (if they exist), horizontal asymptote (if there is one), behavior for large x and and large negative x):
a.
b.
c.
d.
e.
f.
g.
h.
