Textbook Question
Identify each expression as a polynomial or not a polynomial. For each polynomial, give the degree and identify it as a monomial, binomial, trinomial, or none of these. -5x11
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Ch. R - Review of Basic Concepts
Lial13th EditionCollege AlgebraISBN: 9780136881063
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Table of contents
Chapter 1, Problem 11a
Find the domain of each rational expression. (x + 3) / (x - 6)
Verified step by step guidance1
Identify the rational expression given: \(\frac{x + 3}{x - 6}\).
Recall that the domain of a rational expression includes all real numbers except those that make the denominator equal to zero.
Set the denominator equal to zero to find the values to exclude: \(x - 6 = 0\).
Solve the equation \(x - 6 = 0\) to find \(x = 6\).
Conclude that the domain is all real numbers except \(x = 6\), because at \(x = 6\) the denominator becomes zero and the expression is undefined.
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Video duration:
3mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rational Expressions
A rational expression is a fraction where both the numerator and denominator are polynomials. Understanding rational expressions involves knowing how to simplify, evaluate, and analyze them, especially focusing on restrictions caused by the denominator.
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Rationalizing Denominators
Domain of a Function
The domain of a function is the set of all input values (x-values) for which the function is defined. For rational expressions, the domain excludes any values that make the denominator zero, as division by zero is undefined.
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3:51Domain Restrictions of Composed Functions
Finding Restrictions on the Domain
To find the domain of a rational expression, identify values that make the denominator zero and exclude them. For example, setting the denominator equal to zero and solving for x reveals these restricted values.
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3:51Domain Restrictions of Composed Functions
Related Practice
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