Find the domain and range of the function g(x) = V.r² – 8.x. Answer using interval

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Question 1:** Find the domain and range of the function \( g(x) = \sqrt{x^2 - 8x} \). Answer using interval notation.

**Work:** \( g(x) = \sqrt{x^2 - 8x} \)
Transcribed Image Text:**Question 1:** Find the domain and range of the function \( g(x) = \sqrt{x^2 - 8x} \). Answer using interval notation. **Work:** \( g(x) = \sqrt{x^2 - 8x} \)
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The domain of the function: - The "all the values" that go into a function are referred to as a domain. The domain of a function is the set of all the function's possible inputs. Consider this box as a f(x) = 2x function. The domain is just the set of natural numbers when the values x = 1,2,3,4,...are entered, and the output values are referred to as the range.

The range of the function: - The set of all a function's outputs is its range. Example: Consider the function f: A B, where f(x) = 2x and A and B are a collection of natural numbers. A is the domain, while B is the co-domain in this case. The range is then the output of this function. The range is defined as a group of even natural numbers. The domain elements are referred to as pre-images, while the mapped elements of the co-domain are referred to as images. The set of all pictures of the domain's elements (or) the set of all the function's outputs is the range of the function f.

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