Pre-calculus Contents E
      Linear function
      The linear function  f (x) = mx + c
         The graph of the linear function
         Roots or zeros, x- and y-intercepts of a graph
         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 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
         Division of polynomials examples
      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
         Graphing the quadratic function example
      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
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