REFERENCES
[a] Understand the basics of functions and know how to apply them to problemsolving situations.
[i] Identify the mathematical domains and ranges and determine reasonable domain and range values for given situations.
[ii] Know how to manipulate symbols in order to solve problems and use the necessary algebraic skills required to simplify algebraic expressions (factoring, properties of exponents etc.).
[ii] Connect the function notation of y = and ƒ(x) =.
[ii] Analyze situations and formulate systems of equations or inequalities in two or more unknowns to solve problems.
[iii] Interpret and determine the reasonableness of solutions to systems of equations or inequalities.
[iv] Identify and sketch graphs of parent functions, including linear (y = x), quadratic (y = x^{2}), square root (y = √x), inverse (y = 1/x), exponential (y = a^{x}), and logarithmic (y = log_{a}x) functions.
[b] More advanced functions.
[i] Describe a conic section as the intersection of a plane and a cone.
[ii] Identify symmetries from graphs of conic sections and identify the conic section from a given equation.
[iii] Understand that quadratic functions can be represented in different ways and learn to translate among their various representations.
[iv] Determine the reasonable domain and range values of quadratic functions, interpret and determine the reasonableness of solutions to quadratic equations and inequalities.
[v] Relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions.
[iv] Determine a quadratic function from its roots or a graph.
[v] Use characteristics of the quadratic parent function to sketch the related graphs and connect between the y = ax^{2} + bx + c and the y = a(x  h)^{2} + k symbolic representations.
[c] Rational functions.
[i] Formulate equations and inequalities based on rational functions.
[ii] Use quotients to describe the graphs of rational functions, describe limitations on the domains and ranges, and examine asymptotic behavior.
[iii] Determine the reasonable domain and range values of rational functions and determine the reasonableness of solutions rational equations and inequalities.
[iv] Analyze a situation modeled by a rational function, formulate an equation or inequality.
[d] Exponential and logarithmic functions.
[i] Formulate equations and inequalities based on exponential and logarithmic functions.
[ii] Develop the definition of logarithms by exploring and describing the relationship between exponential functions and their inverses.
[iii] Analyze a situation modeled by an exponential function, formulate an equation or inequality.
1.1  Linear Expressions and Equations
Sometimes, you find yourself having to write out your own algebraic
expression based on the wording of a problem.
In that situation, you want to

read the problem carefully,

pick out key words and phrases and determine their equivalent mathematical
meaning,

replace any unknowns with a variable, and

put it all together in an algebraic expression.
The following are some key words and phrases and
their translations:
Addition: sum, plus, add to, more than,
increased by, total 
Subtraction: difference of, minus,
subtracted from, less than, decreased by, less 
Multiplication: product, times, multiply,
twice, of 
Division: quotient divide, into,
ratio 
[1.1.a] Write the phrase as an algebraic expression.
The sum of a number and 10
It looks like the only reference to a mathematical operation is the
word sum  so what operation will we have in this expression?
If you said addition, you are correct.
The phrase 'a number' indicates that it is an unknown number  there
was no specific value given to it. So we will replace the phrase
'a number' with the variable x. We want
to let our variable represent any number that is unknown
Putting everything together, we can translate the given english phrase
with the following algebraic expression:
*'sum' = +
*'a number' = variable X
*'The sum of a number and 10' = X + 10
[1.1.b]
The product of 5 and a number
Again, we are wanting to rewrite this as an algebraic expression, not
evaluate it.
This time, the phrase that correlates with our operation is 'product'
 so what operation will we be doing this time? If you said
multiplication,
you are right on.
Again, we have the phrase 'a number', which again is going to be replaced
with a variable, since we do not know what the number is.
Let’s see what we get for this answer:
*'product' = multiplication
*'a number' = variable X
The product of 5 and a number = 5X
[1.1.c]
3 less than twice a number
First of all, we have the phrase 'less than' which mathematically
translates as subtraction. You need to be careful with this phrase,
it is very tempting to start off with 3 and put your subtraction sign after
the 3. However, think about it, if you want 3 less than something,
you are 3 below it. In order to be 3 below something, you would have to
subtract the 3. So you would not have 3 minus, but minus 3 as PART
of your expression.
The other part of the expression involves the phrase 'twice a number'.
'Twice' translates as two times a number and, as above, we will replace
the phrase 'a number' with our variable x.
Putting this together we get:
*'less than' = 
*'twice' = 2 times
*'a number' = variable X
*'3 less than twice a number' = 3  2X
[1.1.d]
The quotient of 3 and the difference of a number and 2
First of all, the term 'quotient' is going to be replaced with
what mathematical operation? If you said division, you are
right on the mark.
Note how 3 immediately follows the phrase 'the quotient of', this means
that 3 is going to be in the numerator. The phrase that immediately
follows the word 'quotient' is going to be in the numerator of it.
After the word ‘and', you have the phrase 'the difference of a number
and 2'. That is the second part of your quotient which means it will
go in the denominator. And what operation will we have when we do
write that difference down below? I hope you said subtraction.
Let’s see what we get when we put all of this together:
*'quotient' = division
*'difference' = 
*'a number' = variable X
*'The quotient of 3 and the difference of a number and 2' = 3 / [X  2]
1.2  Slope, Intercepts, and SlopeIntercept Form
Straightline equations, or linear equations, graph as straight lines, and have simple variables with no exponents on them.
For example, the linear function, f(x) = mx + b, may be graphed on the x, y plane as the equation,
y = mx + b
In summary