/*! 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 4 Determine which functions are po... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 4

Determine which functions are polynomial functions. For those that are, identify the degree. $$g(x)=6 x^{7}+\pi x^{5}+\frac{2}{3} x$$

Short Answer

Expert verified
The given function \(g(x)=6 x^{7}+\pi x^{5}+\frac{2}{3} x\) is a polynomial function and its degree is 7.

Step by step solution

01

Identify Polynomials

Polynomials are expressions involving a sum of powers of a variable multiplied by coefficients. Specifically, it should be noted that each term in the polynomial consists of a coefficient (a real number) times the variable raised to a non-negative integer power, or exponent. Looking at the given function: \(g(x)=6 x^{7}+\pi x^{5}+\frac{2}{3} x\), it conforms to the definition of a polynomial because all the exponents of variable x are non-negative integers, and the coefficients (which in this case are 6, \( \pi \), and \( \frac{2}{3} \)) are all real numbers.
02

Determine the Degree of the Polynomial

The degree of a polynomial is the highest exponent in the polynomial. In the function \(g(x)=6 x^{7}+\pi x^{5}+\frac{2}{3} x\), the highest exponent is 7 (from the term \(6x^{7}\)). Thus, the degree of this polynomial is 7.

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!

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

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. Write a rational inequality whose solution set is \((-\infty,-4) \cup[3, \infty)\).

Use transformations of \(f(x)=\frac{1}{x}\) or \(f(x)=\frac{1}{x^{2}}\) to graph each rational function. $$g(x)=\frac{1}{x+2}-2$$

You drive from your home to a vacation resort 600 miles away. You return on the same highway. The average velocity on the return trip is 10 miles per hour slower than the average velocity on the outgoing trip. Express the total time required to complete the round trip, \(T\), as a function of the average velocity on the outgoing trip, \(x .\)

a. Find the slant asymptote of the graph of each rational function and \(\mathbf{b} .\) Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{3}+1}{x^{2}+2 x}$$

The equation for \(f\) is given by the simplified expression that results after performing the indicated operation. Write the equation for \(f\) and then graph the function. $$\frac{2}{x^{2}+3 x+2}-\frac{4}{x^{2}+4 x+3}$$
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Discrete Mathematics

Read Explanation

Pure Maths

Read Explanation

Statistics

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.