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
Slope-intercept form of a line
The point-slope 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)
T
he 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
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