Algebra 7 - Bounded versus Unbounded Intervals @MyWhyU

Uploaded July 2012 | Updated September 2026, 3 weeks ago

Bounded intervals may be either open or closed. Closed intervals contain a maximum and minimum number, but why is it impossible to find the maximum or minimum number in an open interval?

Algebra 7 - Bounded versus Unbounded Intervals

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

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Algebra 7 - Bounded versus Unbounded Intervals