/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 84 Find the domain of the function ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 84

Find the domain of the function given by each equation. $$ g(x)=x^{2}+3 $$

Short Answer

Expert verified
The domain of the function is \((-\infty, \infty)\).

Step by step solution

01

Identify the Type of Function

The given function is a polynomial function, specifically a quadratic function. Polynomial functions are defined for all real numbers.
02

Determine the Domain of the Polynomial Function

Since polynomial functions are defined for all real numbers, the domain of the function is all real numbers.
03

Write the Domain in Interval Notation

Express the domain using interval notation, which is \((-\infty, \infty)\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Polynomial Functions
A polynomial function is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. The simplest example is a linear function like \(f(x) = 2x + 3\), where the highest power of \(x\) is 1. When we increase the power of \(x\), we get more complex polynomial functions. For example, a quadratic function like \(g(x) = x^{2} + 3\) has a highest power of 2. Polynomial functions are very flexible and can model a variety of real-world situations. They are also continuous and smooth, making them easy to work with.
Interval Notation
Interval notation is a way of writing subsets of the real number line. It is often used to describe the domain and range of functions. For example, the interval \( (a, b) \) represents all real numbers between \(a\) and \(b\), not including \(a\) and \(b\). Similarly, \( [a, b] \) includes both \(a\) and \(b\). If we want to describe the domain of a polynomial function like \( g(x) = x^{2} + 3 \), we use the interval \( (-\rightarrow, \rightarrow )\), indicating that any real number is acceptable as input.
Real Numbers
Real numbers include all the numbers you can think of: positive numbers, negative numbers, and zero. They can be written as decimals or fractions. Real numbers are used to measure continuous quantities, and they are the foundation for many mathematical concepts. When we talk about the domain of a function, we are usually looking for all real numbers that can be plugged into the function without causing any problems (like division by zero). For polynomial functions, all real numbers can be used. In interval notation, this is represented as \( (-\rightarrow, \rightarrow )\).

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For the function given by \(n(z)=a b+w z,\) what is the independent variable? How can you tell?

Assume that \(r, p,\) and \(s\) are nonzero constants and that \(x\) and \(y\) are variables. Determine whether each equation is linear. $$ r x+3 y=p^{2}-s $$

Determine whether each equation is linear. Find the slope of any nonvertical lines. $$ 3 y=7(2 x-4) $$

Graph equation after plotting at least 10 points. \(y=x^{3} ;\) use \(x\) -values from \(-2\) to 2

Find the domain of the function given by each equation. $$ g(x)=\frac{1}{2} x $$
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Probability and Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.