Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 1

Chapter 3, Problem 1

Find the domain of each function. f(x)=3(x-4)

Verified step by step guidance

Identify the function given: \(f(x) = 3(x - 4)\).

Recall that the domain of a function is the set of all possible input values (\(x\)) for which the function is defined.

Since \(f(x) = 3(x - 4)\) is a linear function (a polynomial of degree 1), it is defined for all real numbers.

Therefore, there are no restrictions such as division by zero or square roots of negative numbers that would limit the domain.

Conclude that the domain of \(f(x)\) is all real numbers, which can be written in interval notation as \((-\infty, \infty)\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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. It determines where the function produces valid outputs without causing undefined expressions like division by zero or square roots of negative numbers.

Polynomial Functions

Polynomial functions are expressions involving variables raised to whole-number exponents combined using addition, subtraction, and multiplication. They are defined for all real numbers, meaning their domain is typically all real numbers unless otherwise restricted.

Function Notation and Evaluation

Function notation, such as f(x), represents a function with input x. Understanding how to substitute values into the function and simplify the expression is essential for analyzing the function's behavior and determining its domain.

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