Mathematics 120 (Precalculus)

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.