Pre-calculus Contents E  f (x) = mx + c
Roots or zeros, x- and y-intercepts of a graph Absolute value functions and equations
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 the straight line
Definition of the slope of a line
Slope-intercept form of a line
The point-slope form of a line
The two point form of the equation of a line
Parallel and perpendicular lines
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
The source or the original polynomial function
Translating (parallel shifting) of the source polynomial function
Coordinates of translations and their role in the polynomial expression Roots or zeros of polynomial function
Vieta's formulas Graphing polynomial functions
Zero polynomial
Constant function Linear function Quadratic function and equation
Transition of the quadratic polynomial from the general to source form and vice versa
The zeros or the roots of the quadratic function
Vertex (the turning point, maximum or minimum) - coordinates of translations Cubic function
Transformation of the cubic polynomial from the general to source form and vice versa
Coordinates of the point of inflection coincide with the coordinates of translations
The source cubic functions are odd functions There are three types of the cubic functions - the classification criteria diagram
The graphs of the source cubic functions Translated cubic functions
Translated cubic function, the type 1 - the tangent line at the point of inflection is horizontal
Translated cubic function, the type 2/1 - no turning points, the tangent at inflection is a slant line
Translated cubic function, the type 2/2 - with two turning points, the tangent at inflection is a slant line
Graphing a cubic function examples
Graphing translated cubic function type 2/2 Quartic function
Transformation of the quartic polynomial from the general to source form and vice versa
The coordinates of translations formulas
The values of the coefficients, a2 and a1 of the source quartic function y = a4x4 + a2x2 + a1x The basic classification criteria diagram for quartic function
The graphs of quartic functions and their characteristic points
The quartic  type 1,   y - y0 = a4(x - x0)4a2 = 0 and a1 = 0
The quartic  type 2,   y - y0 = a4(x - x0)4 + a1(x - x0)a2 = 0
The quartic  type 3/1,   y - y0 = a4(x - x0)4 + a2(x - x0)2a1 = 0 and  a4a2 > 0
The quartic  type 3/2,   y - y0 = a4(x - x0)4 + a2(x - x0)2a1 = 0 and  a4a2 < 0 The graphs and classification criteria diagram for the quartics types 4/1 to 4/6,
y - y0 = a4(x - x0)4 + a2(x - x0)2 + a1(x - x0)
The zeros and the abscissas of the turning points of the source quartics types 4/1 to 4/6
Graphing the quartic polynomial, example   Pre-calculus Contents 