
College
algebra contents C






Linear
Function

The linear function
f
(x)
= mx + c 
The graph of
the linear function 
Properties
of the linear function 
Absolute
Value Functions and Equations 
The graph
of the
absolute value function f
(x)
= 
x
 
The graph of absolute value of a linear function
f
(x) =
 ax+
b 

Linear equation with
absolute value, graphic solution 
Absolute
Value Inequalities 
Solving linear inequalities with absolute value 
Equations
of Straight Line

Slope of a line 
Slopeintercept form
of a line 
The pointslope form
of a line 
The two points form of
the equation of a line 
Parallel and
perpendicular lines 
Simultaneous
Linear Equations

System of two linear
equations in two unknowns (variables)

The
system has, a single solution, no solution or has infinitely many
solutions

Solving systems of equations

Substitution and comparison method

Addition or elimination method

System of
linear equations word problems

Solving systems of equations graphically

Independent equations, inconsistent equations and dependent
equations

Cramer’s rule (using determinants) to solve systems of
linear equations

Solving system of two equations in two unknowns using
Cramer's rule

Solving system of three equations in three unknowns using
Cramer's rule

Method of expanding a determinant of a rank n to
cofactors 
Systems
of Linear Inequalities

Solving and graphing systems of
linear inequalities

Solving and graphing systems of
linear inequalities in two variables

Rational
Inequalities 
Method of solving rational inequalities

The graph of the translated equilateral (or rectangular) hyperbola

Polynomial
and/or Polynomial Functions and Equations 
Definition
of a polynomial or polynomial function 
Division
of polynomials 
Factoring polynomials and solving polynomial equations by
factoring 
Solving quadratic and
cubic equations by factoring, examples 
Polynomial
functions 
Source or original polynomial function 
Translating (parallel shifting) of the polynomial function 
Coordinates of translations and their role in the polynomial
expression 
Transformations of the polynomial function applied to the
quadratic and cubic functions 
Roots
or zeros of polynomial function 
Graphing
polynomial functions 
Zero polynomial 
Constant function 
Linear function 
Quadratic
Function and Equation 
The graph of quadratic
function 
Translated form of
quadratic function 
The sum and product of
the roots 
Vertex (the turning point, maximum or minimum)  coordinates of
translations 
Transformations of the graph of the quadratic function 
Quadratic equation
word problems 
Cubic
Functions 
Graphs of cubic functions 
Graphing a cubic function, example 
Sigma
notation of the polynomial 
Coefficients of the source polynomial in the form of a recursive
formula

Coefficients
of the source polynomial function are related to its derivative
at x_{0} 








College
algebra contents 



Copyright
© 2004  2020, Nabla Ltd. All rights reserved. 