Uploaded October 2011 | Updated September 2026, 3 weeks ago

A humorous look at the mathematics behind infinite series.

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Algebra 68 - Converting Between General and Vertex Form

Algebra 9 - Cartesian Products, Ordered Pairs and Triples

Algebra 98 - How Logarithms Are Used Today

Pre-Algebra 27 - Raising Exponential Expressions to Powers

Pre-Algebra 22 - Exponents of One, Zero, and Negative

Algebra 71 - Solving Difference of Squares Quadratic Equations

Algebra 89 - Multiplying Polynomial Functions

$Algebra 91 - Rational Functions and Vertical Asymptotes A rational function is any function that can be written as a fraction whose numerator and denominator are polynomials. Rational functions include a broad range of possibilities. For example, since a polynomial can be a constant, a rational functions numerator and denominator can both be constants, in which case the rational function is simply a constant function. Unlike polynomial functions whose domains include all real numbers, in this lecture we show that any x value that causes the functions denominator to be zero will be excluded from the functions domain. These excluded x values produce missing points in the functions graph, and these missing points may be the locations of vertical asymptotes. Even though a functions graph can approach infinitely close to a vertical asymptote, it can never intersect that asymptote, since when the denominators value is zero, the functions value is undefined. A vertical asymptote is therefore a vertical line that a functions graph can approach arbitrarily close to, but can never intersect.$ $Pre-Algebra 14 - Creating Common Denominators Addition and subtraction of fractions with different denominators requires creating a common denominator. Using the number line, this mysterious process can be easily visualized.$

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