**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) = x^{2} - x b. f(x) = -x^{3} + x^{2
}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) = -x^{2} + 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) = x^{3} + 8

c. y = s(x) = -x^{2 }+ 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) = -x^{3}

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 = -3x^{3}

6. What are the potential rational roots of the following polynomial equations?

a. x^{3} -4x + 3 = 0

b. x^{4} - x^{3} - 6x^{2} - x + 6 = 0

c. 3x^{3} - 5x^{2} - 5 = 0

7. Use synthetic division to check:

a. Is 2 a root of x^{4} - x^{3} - 6x^{2} - x + 6 = 0?

b. The quotient when x^{4} - x^{3} - 6x^{2} - x + 6 is divided by x - 4.

c. The remainder when x^{4} - x^{3} - 6x^{2} - x + 6 is divided by x +3.

d. Is x-3 a factor of x^{4} - x^{3} - 6x^{2} + 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.