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