Graph. f(x)=(x^2-1)/(x-1)

Name: Problem 35, Chapter 0: Calculus and Its Applications
Uploaded: 2020-10-22T15:10:54-08:00
Duration: 1 min 8 s
Channel: Linh Vu
Description: Graph. f(x)=(x^2-1)/(x-1)

Key Concepts

Removable Discontinuities

A removable discontinuity occurs when a common factor in the numerator and denominator of a rational function cancels out, leaving an undefined point where the function could be 'fixed' by appropriately redefining it. This concept explains why a function might behave like a simpler function almost everywhere, except for specific isolated points where the function is not defined.

Domain Restrictions

Domain restrictions refer to the set of input values for which a function is defined. In rational functions, this usually means excluding values that cause the denominator to be zero. Properly identifying domain restrictions is fundamental for accurately graphing and understanding the behavior of the function.

Rational Functions

Rational functions are expressions formed by the ratio of two polynomials. Understanding these functions involves analyzing their domains, potential asymptotes, and discontinuities. Their graphs often exhibit features such as vertical asymptotes or holes, which are key to interpreting behavior at specific input values.

Polynomial Factoring

Polynomial factoring is the process of breaking down a polynomial into a product of simpler polynomials. This technique is essential for simplifying rational functions and can reveal common factors in the numerator and denominator, which may cancel out to simplify the expression or indicate a removable discontinuity.

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