/*! 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 25 Describe the right-hand and left... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 25

Describe the right-hand and left-hand behavior of the graph of the polynomial function. \(f(x)=-2.1 x^{5}+4 x^{3}-2\)

Short Answer

Expert verified
The graph of the polynomial decreases (\(f(x) \rightarrow -\infty\)) as \(x\) increases (\(x \rightarrow \infty\)) (right-hand behavior), and increases (\(f(x) \rightarrow \infty\)) as \(x\) decreases (\(x \rightarrow -\infty\)) (left-hand behavior).

Step by step solution

01

Identify Degree & Leading Coefficient

Identify the degree of the polynomial and its leading coefficient. The degree of the polynomial function \(f(x)=-2.1 x^{5}+4 x^{3}-2\) is 5, and the leading coefficient is -2.1.
02

Determine Right-hand Behavior

Analyze the right-hand behavior of the graph. As \(x\) approaches infinity (\(x \rightarrow \infty\)) the function behavior depends on the degree and the leading coefficient. If the degree is odd and the leading coefficient is negative, as in this case, then as \(x\) increases, \(f(x)\) decreases. So, \(f(x) \rightarrow -\infty\) as \(x \rightarrow \infty\). This means the graph descends to the right.
03

Determine Left-hand Behavior

Analyze the left-hand behavior of the graph. In general, as \(x\) approaches negative infinity (\(x \rightarrow -\infty\)) the function behavior is inverse to the right-hand behavior for odd degree polynomials. Thus, for the given polynomial function, since the degree is odd and the leading coefficient is negative, as \(x\) decreases, \(f(x)\) increases. So, \(f(x) \rightarrow \infty\) as \(x \rightarrow -\infty\). This means the graph ascends to the left.

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

Solve the inequality and graph the solution on the real number line. \(\frac{3 x}{x-1} \leq \frac{x}{x+4}+3\)

Solve the inequality and write the solution set in interval notation. \(x^{3}-4 x \geq 0\)

Solve the inequality and graph the solution on the real number line. . \(\frac{x+12}{x+2}-3 \geq 0\)

Use a graphing utility to graph the rational function. Give the domain of the function and identify any asymptotes. Then zoom out sufficiently far so that the graph appears as a line. Identify the line. \(f(x)=\frac{x^{2}+5 x+8}{x+3}\)

Solve the inequality and graph the solution on the real number line. \(\frac{5}{x-6}>\frac{3}{x+2}\)
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Probability and 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.