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## Precalc Notes

 Functions, Vocabulary Quadratic Functions Exponent & Log Laws Orientation, ... Higher Order Polynomials Trig Functions, "Before Unit Circle" Calculator Resources Rationals Trig Functions, "Unit Circle & On" Lines Log & Exponential Functions Trig Cheat Sheet

## Higher Order Polynomial Functions Definition & Notation Simple definition (for algebra I and geometry):   polynomial   Precalc definition: an algebraic expression or function, named by its highest degree, produced by the MULTIPLICATION of constants, monomials, binomials, ..., with the use of one variable x,   anxn + an-1xn-1 + an-2xn-2 + ... +a2x2 + a1x1 + a0x0,   in which the constants an, an-1, an-2, ... , a2, a1, a0 are real, and serve as coefficients or the constant term, and in which all exponent of x are counting numbers.

Notes
Polynomial Functions: Notes Definition & Notation
Polynomial Computation
Possible Roots
Complex Roots
Polynomial Functions How to sketch a polynomial function
Examples of sketching polynomial functions
Problems to sketch and their solution
Intercepts/Roots/Factors Vocabulary & Images Games and Manipulatives
Who Has? Polynomial F(x) Game ## Rational Functions Definition & Notation Precalc definition: an algebraic expression or function, produced by the DIVISION of polynomials, with the use of one variable x -- fraction expressions or fraction functions   anxn + an-1xn-1 + an-2xn-2 + ... +a2x2 + a1x1 + a0x0 __________________________________________ bnxn + bn-1xn-1 + bn-2xn-2 + ... +b2x2 + b1x1 + b0x0   in which the constants an, an-1, an-2, ... , a2, a1, a0, bn, bn-1, bn-2, ... , b2, b1, b0 are real, and serve as coefficients or the constant term, and in which all exponent of x are counting numbers.

Notes
Rational Functions a list of things to do when sketching a rational function
two examples of sketching rational functions
a problems to try and their solution
Features of a Rational Function Sketch f(x) = [ (x2 - 4)(x + 3)] / [(x+2)(x-1)] Synthetic division & long division to find zeros
to rewrite a rational function to find horizontal and other asymptotes and
to determine the end behavior.

Games
Who Has? Rat'l F(x)   Visit the Interactive Sketch Pad Material On This Topic Polynomial and Rational Functions parabola   -- Multi page: 2 parabolas: 1 in general form, 1 in standard forms,     * both generated by equations defined by parameters.     * WITH SHOW/HIDE ACTION BUTTON     * graphs of 2 parabolas: 1 in general form, 1 in standard forms,     * 1 parabola, set a, then generat parabola w/2 points.     * 1 parabola controlled by 3 points, used for determinant analysis     * 1 vertical axis of symmetry, 1 horizontal "axis of symmetry" TracePoly   -- drag point f(x) to state and show new ( x, f(x)) recipfx   -- graph of parameter-defined reciprocal function,     * with slide-able tangent line,     * VERTICAL ASYMPTOTE MUST BE POSITIONED BY USER! Spread Sheets -- Dynamic Computation polynomial spreadsheet --     graph a polynomial function written in factored form     complete synthetic division synthetic division spreadsheet -- just complete synthetic division of a polynomial or of a quadratic by a linear binomial rational function spread sheet Graph and table of (Axm)/(Bxn)     Watch the power of the top or bottom equal or dominate the other.     Examine hoirzontal asymptotes or infinite increase or decrease.     Think endbehavior and explore.     Graph and table of rational function, polynomial A(x) divided by B(x).     Examine asymptotes.     Examine the role of factors A(x) and 1/B(x).     Graph and table of rational functions written as A(x) / B(x) + C(x)     Really play with C(x), the asymptote     Complete synthetic division and rewrite of quotient and remainder.

 Functions, Vocabulary Quadratic Functions Exponent & Log Laws Orientation, ... Higher Order Polynomials Trig Functions, "Before Unit Circle" Calculator Resources Rationals Trig Functions, "Unit Circle & On" Lines Log & Exponential Functions Trig Cheat Sheet         © 8/2019, 9/2022, A. (A2) Azzolino www.mathnstuff.com/math/precalc/pnotes3.htm