User:Mjmohio/College Algebra (Ohio TAGS)

College Algebra (Ohio TAGS)
This course is designed to follow the State of Ohio's Transfer Assurance Guidelines (TAGS) for College Algebra. You cannot actually get credit for this course in Ohio, but you will know that you are studying the correct material. Good uses of this course include:
 * A student about to start college learning here so they can take a placement test that allows them to skip College Algebra completely and start with a higher level course.
 * A high school student getting a head start.
 * A college student supplementing their college algebra.
 * A returning student refreshing their knowledge of the subject.

To learn mathematics on your own, you need to hold yourself to a high standard. If you do not understand something, you cannot just skip it; instead keep working on it. If you do not know how to do an exercise, you cannot look at the answer and try to work backwards; instead go back to the material and figure it out. The superficial understanding you would get by just clicking through this course will not enable you to actually do anything, and in particular will not prepare you for the next course.

The guidelines for College Algebra are organized by
 * The successful College Algebra student should be able to:

so that is how we organize this course. All references in the guidelines to functions are footnoted to:


 * This course should consider the following types of functions:
 * polynomial
 * rational
 * root/radical/power
 * exponential and logarithmic
 * piece-wise defined

Represent functions verbally, numerically, graphically, and algebraically.
Wikipedia resources: function (mathematics), list of mathematical functions, graph of a function .

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View a function as a set of ordered pairs or a correspondence between two sets.
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Find the domain and range of functions.
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Perform translations and dilations of functions.
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Perform operations (addition, subtraction, multiplication, division, composition) with functions.
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Use functions to model a variety of situations.
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Solve equations, including application problems.
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Solve systems of linear equations, including systems and application problems.
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Solve nonlinear inequalities.
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Apply the factor theorem, the remainder theorem, and the rational roots theorem, including application problems.
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Find inverses of functions and relate the graph of a function to the graph of its inverse.
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==== Analyze the graph of a function to answer questions about the function (such as intercepts, domain, range, intervals where the function is increasing or decreasing, possible algebraic definitions, etc.) ====

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Exercise Template
Insert exercise pages with answers hidden like:

blah blah blah question? Solution: No, 2 is not a member of the orginal set.

$$\pi \theta2 $$

Quiz template
Insert quiz pages with quizzes like:

{LU decomposition is - A name of the algorithm to solve any linear systems + a matrix decomposition which writes a matrix as the product of a lower triangular matrix and an upper triangular matrix - A the program to solve any linear systems - None of those
 * type=""}

{Is it true that any matrix can be factorize to LU form without pivoting? - Yes + No
 * type=""}

{ The determinant of $$\left[\begin{array}{c c}3 & 4 \\2 & 1\end{array} \right]$$ is { -5 _3 }.
 * type="{}"}

{
 * type="{}"}

$$ \displaystyle \ y_1 = $$ { 4 } $$ \displaystyle \ y_2 = $$ { -1 } $$ \displaystyle \ y_3 = $$ { 6 }

Next, we have Ux = y

$$ \begin{bmatrix} 2&-1&3\\0&4&-5\\0&0&6\end{bmatrix}$$ X $$\begin{bmatrix} x_1\\x_2\\x_3\end{bmatrix} $$ = $$\begin{bmatrix} y_1\\y_2\\y_3\end{bmatrix} $$

Use backward substitution we have:

$$ \displaystyle \ x_1 = $$ { 1 } $$ \displaystyle \ x_2 = $$ { 1 } $$ \displaystyle \ x_3 = $$ { 1 }