/*! 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 80 Explain how to use the Leading C... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 80

Explain how to use the Leading Coefficient Test to determine the end behavior of a polynomial function.

Short Answer

Expert verified
The end behavior of a polynomial function can be determined by the leading coefficient test, which checks the degree of the function and the sign of its leading coefficient. Depending on these two factors, the test predicts whether the function will rise or fall to the right and left.

Step by step solution

01

Understand Leading Coefficient Test

The leading coefficient test is used to determine the end behavior of a function. For a polynomial function, the highest degree term is the leading term - the term which has the largest exponent, and its coefficient is the leading coefficient. The end behavior of a polynomial function is determined by the degree of the leading term and its coefficient.
02

Determine the degree and the leading coefficient

Identify the leading term in the polynomial, which is the term with the highest power. The coefficient of this term is the leading coefficient and the exponent is the degree of the polynomial.
03

Apply the Leading Coefficient Test

Apply the test. If the degree is odd and the leading coefficient is positive, the graph will rise to the right and fall to the left. If the degree is odd and the leading coefficient is negative, the graph will fall to the right and rise to the left. If the degree is even and the leading coefficient is positive, the graph will rise to both the left and the right. And lastly, if the degree is even and the leading coefficient is negative, the graph will fall to both the left and the right.

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

Use the four-step procedure for solving variation problems given on page 424 to solve. \(y\) varies jointly as \(a\) and \(b\) and inversely as the square root of \(c . y=12\) when \(a=3, b=2,\) and \(c=25 .\) Find \(y\) when \(a=5, b=3,\) and \(c=9\).

Galileo's telescope brought about revolutionary changes in astronomy. A comparable leap in our ability to observe the universe took place as a result of the Hubble Space Telescope. The space telescope was able to see stars and galaxies whose brightness is \(\frac{1}{50}\) of the faintest objects observable using ground-based telescopes. Use the fact that the brightness of a point source, such as a star, varies inversely as the square of its distance from an observer to show that the space telescope was able to see about seven times farther than a ground-based telescope.

Is every rational function a polynomial function? Why or why not? Does a true statement result if the two adjectives rational and polynomial are reversed? Explain.

The number of houses that can be served by a water pipe varies directly as the square of the diameter of the pipe. A water pipe that has a 10 -centimeter diameter can supply 50 houses. a. How many houses can be served by a water pipe that has a 30 -centimeter diameter? b. What size water pipe is needed for a new subdivision of 1250 houses?

If you are given the equation of a rational function, explain how to find the horizontal asymptote, if any, of the function's graph.
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Logic and Functions

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.