**Take Home Quiz ( Real Numbers )**

(1) Given x > 0 and y < 0 de termine the sign of y(y - x)
and
Also, if x - y > 0 then

determine the sign of

(2) Express the statement as an inequality:

The absolute value of x - 3 is greater than 8 and less than 16.

(3) Express
as a fraction and then express
as a repeating decimal .

(4) Using the Properties of the Real Numbers, solve the
equation 4 x = 7 x - 3.

**Take Home Quiz (Exp onents and Radicals )**

(1) Simplify

(2) Simplify

(3) Simplify

(4) Simplify

(5) Given
rationalize the denominator .

(6) Given
rationalize the numerator .

(7) Given
rationalize the denominator.

**Take Home Quiz (Quadratic Functions)**

(1) Express
in the form
Sketch the graph of f and label the x and y intercepts, the

zeros, the vertex , and the line of symmetry .

(2) Given constants b and e, express
in the form
Sketch
the graph of f and label the

x and y intercepts, the zeros , the vertex, and the line of symmetry.

(3) Given
and
find

(4) Solve the equation
given
and

(5) Determine the domain of
given
and
Justify your statement.

**Take Home Quiz (Properties of Division)**

(1) Use long division to divide

(2) Use synthetic division to divide

(3) Express the function in the form
for the given value of k, and demonstrate that

(a) f (x) = -4 x^{3} + 6 x^{2} + 12 x + 4 with

(b) f (x) = -3 x^{3} + 8 x^{2} + 10 x - 8 with

(4) Find a real number k such that x - 3 is a factor of
x ^{4} - 5 x^{3} - k x^{2} + 18 k + 18.

(5) Find the values for k such that f (x) = k^{2} x^{3} - 4 k
x + 3 is divisible by the linear polynomial x - 1.

(6) Show that x - k is not a factor of f (x) = -x^{4} - 3
x^{2} - 2 for any real number k.

(7) Construct a cubic polynomial function with
x-intercepts of 1, 2, and 3 which passes through the point (4, 12).

**Take Home Quiz (Functions)**

(1) Determine a so that the lines 2 x - 3 y = 9 and x - 3
y = -11 are parallel.

(2) Determine a so that the equation through the points
(a, 3) and
is 2 x - 4 y = -11.

(3) Determine a so that the equation through the points
(a, 3) and (-a, 4) is x + 6 y = 21.

(4) Given f (x) = 2 x^{2} + 3 x - 4 find

(5) State the domain and range of the function

(6) State the domain of the function

**Take Home Quiz (Inverse Functions)**

(1) Determine whether the fol lowing functions are
one-to-one.

(a) f (x) = x^{2} + 4

(b) f (x) = 2 x^{3} - 4

(c) f (x) = -54 + 54 x - 15 x^{2} + 2 x^{3}

(d)

(2) Determine whether or not the given functions are
inverses of each other or not.

(a) f (x) = x^{3} - 4 and

(b) f (x) = x^{2} + 5, x ≤ 0 and

(3) Find the inverse of the given function, it if exists.

(b) f (x) = (1x^{3} + 1)^{5}

(c) f (x) = x^{2} - 6 x, x ≥ 3

**Take Home Quiz (Exponential and Logarithmic Functions )**

(1) True or False? For those which are true if the domain
is restricted, give the domain; for those that are false, give the

correct equality.

(2) (Exponential and Logarithmic Equations) Solve the
following equations for real x and give the number of solutions

you find for each one. Also clearly state any extraneous solutions that you find
for each one .

(3) (Modeling Population) Based on the estimate that there
are 10 billion acres of land of Earth, and that each acre can

produce enough food to feed 4 people, some demographers believe that the Earth
can support a population of no more

than 40 billion people. The population of the Earth reached approximately 5
billion in 1986 and 6 billion in 1999. If the

population of the Earth is growing according to the formula
where
t is the time after the population is P_{0}

and r is the growth rate, when will the population reach the theoretical limit
of 40 billion?