Answer all assigned exercises, and show all work.
1. Solve each equation. (See section 1.1, Examples 1 and 2.) [4 points]
a.
b.
4(2 x 1) 6 (2 x 4)
1
x2
(2 x 5)
15
9
2. Solve each formula for the individual variable. Assume that the denominator is not 0 i
Commentary for Section 1.7
Keep the following key points in mind when studying section 1.7.
1
An inequality is when one expression is greater than, greater than or equal to, less than,
or less than or equal to another. Properties of inequalities are simil
Commentary for Section 2.1
Keep the following key points in mind when studying section 2.1.
1
An equation in two variables, such as x and y, is a relationship between different values
of the variables. We can think of these relationships as a set of order
Commentary for Section 1.3
Keep the following key points in mind when studying section 1.3.
1
Section 1.3 introduces us to a new number called i.
2
Numbers of the form a + bi are called complex numbers. Complex numbers have two
parts. The a is a real numb
Commentary for Section 3.6
Keep the following key points in mind when studying section 3.6.
1
Variation is a technique for directly or indirectly relating a polynomial to an independent
variable. We often use this technique in physics, economics, and othe
Commentary for Section 3.4
Keep the following key points in mind when studying section 3.4.
1
The methods presented in section 3.4 for graphinc functions are generalizations of the
techniques used previously to graph linear and quadratic functions.
2
A co
Commentary for Section 2.8
Keep the following key points in mind when studying section 2.8.
1
Section 2.8 discusses methods of adding, subtracting, multiplying, and dividing
functions. You can only add, subtract, multiply, and divide functions that have t
Commentary for Sections 1.4 and 1.5
Keep the following key points in mind when studying sections 1.4 and 1.5.
1
has i and i as solutions. now has two solutions: i and i.
2
has two solutions in its solution set, , when When the solution set includes only o
Commentary for Section 3.1
Keep the following key points in mind when studying section 3.1.
1
A quadratic function can be written as
2
When graphed, quadratic functions have parabolic shapes.
3
We use completing the square in finding the zeros of a quadra
Commentary for Section 2.7
Keep the following key points in mind when studying section 2.7.
1
Since we can think of functions as graphs, we are able to use geometric notions and
concepts in describing graphs. Specifically, by altering the equation we can
Commentary for Section 4.1
Keep the following key points in mind when studying section 4.1.
1
Inverse functions are created from a known function when we interchange the xs and ys
of the function. This is equivalent to interchanging the values in the seco
Commentary for Section 2.3
Keep the following key points in mind when studying section 2.3.
1
A function is a specific type of equation or a set of ordered pairs with a restriction. The
restriction is that for every value in the first tuple, there can be
Commentary for Section 2.6
Keep the following key points in mind when studying section 2.6.
1
A function is continuous over an interval if the graph of the function can be drawn
without lifting your pen from the paper. The concept of continuity is very im
Commentary for Section 1.2
Keep the following key points in mind when studying section 1.2.
1
The key to solving verbal problems is to translate from English into the language of
algebra. We use the language of algebra to find the solution set.
2
Review t
Commentary for Section 2.4
Keep the following key points in mind when studying section 2.4.
1
A linear function is a special type of function. When graphed it looks like a line, but
not all pictures of lines are linear functions. Vertical lines, for examp
Commentary for Section 2.5
Keep the following key points in mind when studying section 2.5.
1
Point-slope formAll you need to know for the point-slope form of the equation of
a straight line is the slope of the line, usually represented by m, and a point
Commentary for Section 3.3
Keep the following key points in mind when studying section 3.3.
1
The factor theorem states that if the remainder when is divided by is 0. This means that
is a factor. The converse is also true. In other words, if is a factor o
Commentary for Section 3.2
Keep the following key points in mind when studying section 3.2.
1
Section 3.2 introduces the division of one polynomial by another. Be sure to review the
concepts of long division of real numbers, since the concepts presented i
Commentary for Section 1.6
Keep the following key points in mind when studying section 1.6.
1
Not every equation is linear or quadratic. However, sometimes when you are lucky or
doing problems in the text you can convert a problem to a linear or quadratic
Commentary for Section 1.8
Keep the following key points in mind when studying section 1.8.
1
Absolute value equations and inequalities need to be solved with some care. Focus on
the Properties of Absolute Value on page 159 of the text. Note that techniqu
Non-removable discontinuity @ x=1 and @ x=-2.
Non-removable discontinuity at every n value for x
Function is continuous everywhere
F(x) is continuous (-, -2) and (2,)
Focusing at x= /2 , the limit goes to +, as x approaches /2 from either the left or righ
22) s(t)=-4.9t2 + 12t -3
s(t)= rate of change of velocity= -9.8t +12
s(t)= acceleration= -9.8
3.8
24) Suppose that you are blowing up a balloon by adding air at the rate of 1f 3/s. If the balloon maintains
a spherical shape, the volume and radius are rela
Ratio and proportion are used in many different ways in everyday life. Describe two real life
applications where ratios and proportions are applied. If you have ever applied ratios or
proportions to problem solve in your everyday life please feel free to
The United States uses a unit system different from a large majority of the world. This
discussion activity focuses on the metric system and whether the United States should
convert to that system of measurement.
1. Do you see this to be an advantage or d
George Polya has four guidelines that are used to assist with problem solving. These
guidelines are to understand the problem, devise a plan to solve the problem, carry out the
plan, and lastly to check the results. I noticed that I use math more than I t
How has consumer debt changed over the past few generations?
The increased cost of living has overtaken income growth over the past few
generations. Median household income has grown 28% since 2003, but expenses
have outpaced it meaningfully. Medical cos
Assignment 9
Complete the following textbook exercises, and submit them to your mentor for correction and
grading.
Section 11.1, pages 755756: exercises 2, 8, 10, 12, 20, 22, 36
2. Which of these graphs are trees?
All except c and e are trees.
8. What is
Complete the following textbook exercises, and submit them to your mentor for correction and
grading.
Section 1.4, page 53: exercises 8(b, d), 12(d, f, g), 16(b, c, d)
8. Translate these statements into English, where R(x) is x is a rabbit and H(x) is x
Assignment 10
Complete the following textbook exercises, and submit them to your mentor for correction and
grading.
Section 12.1, page 818: exercises 2, 6, 10, 24, 28
2. Find the values, if any, of the Boolean variable x that satisfy these equations.
a)