Determine all values of x at which the function is discontinuous. f(x)=(x^2-3 x+2)/(x^2-2 x)

Name: Problem 60, Chapter 2: Applied Calculus for the Managerial, Life, and Social Sciences
Uploaded: 2021-05-16T04:00:58-08:00
Duration: 1 min 51 s
Channel: Himanshu Kushwaha
Description: Determine all values of x at which the function is discontinuous. f(x)=(x^2-3 x+2)/(x^2-2 x)

step 1 f of x equal to x square negative 3x plus 2 upon x square negative 2x so here determine all the

Determine all values of x at which the function is...

Key Concepts

Rational Functions

A rational function is a function represented by the ratio of two polynomials. Its domain consists of all real numbers except those that cause the denominator to equal zero, and understanding this is critical for determining where the function may be undefined or discontinuous.

Domain Restrictions in Rational Functions

When analyzing rational functions, it is essential to identify the values of the variable that make the denominator equal to zero because these values are not part of the function’s domain. Recognizing these restrictions helps in pinpointing potential discontinuities.

Factorization

Factorization is the process of breaking down a polynomial into a product of simpler polynomials, which can reveal common factors in the numerator and denominator. In rational functions, this technique is used to simplify the function and further analyze the nature of any discontinuities.

Removable Discontinuities and Vertical Asymptotes

Discontinuities in rational functions come in two primary types: removable discontinuities, which occur when a common factor cancels out between the numerator and denominator, and vertical asymptotes, which occur when the denominator is zero and no cancellation is possible. Distinguishing between these types is key to understanding the behavior of the function at the points where it is undefined.

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