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Find the domain of each function. g(x) = 2/(x+5)
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Ch. 2 - Functions and Graphs
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 3, Problema 5
Find the domain of each function. f(x) = x² - 2x - 15
Guida verificata passo dopo passo1
Identify the type of function given. Here, the function is a polynomial: \(f(x) = x^{2} - 2x - 15\).
Recall that polynomial functions are defined for all real numbers because there are no restrictions such as division by zero or square roots of negative numbers.
Since there are no denominators or even roots in the function, there are no values of \(x\) that would make the function undefined.
Therefore, the domain of the function is all real numbers, which can be expressed in interval notation as \((-\infty, \infty)\).
Summarize the domain: \(\text{Domain} = \{ x \mid x \in \mathbb{R} \}\) or \((-\infty, \infty)\).
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Domain of a Function
The domain of a function is the set of all possible input values (x-values) for which the function is defined. For polynomial functions like f(x) = x² - 2x - 15, the domain typically includes all real numbers because polynomials are defined everywhere on the real number line.
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3:51
Domain Restrictions of Composed Functions
Polynomial Functions
Polynomial functions are expressions involving variables raised to whole-number exponents combined using addition, subtraction, and multiplication. They are continuous and defined for all real numbers, meaning their domain is usually all real numbers unless otherwise restricted.
Video consigliato:
06:04Introduction to Polynomial Functions
Function Notation and Evaluation
Function notation, such as f(x), represents a function with input x. Understanding how to interpret and evaluate functions helps in determining the domain by identifying any restrictions on x that would make the function undefined.
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4:26Evaluating Composed Functions
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