/*! 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 54 Create a function whose graph ha... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 54

Create a function whose graph has the given characteristics. (There are many correct answers.) Vertical asymptote: \(x=-3\) Horizontal asymptote: None

Short Answer

Expert verified
The function \(F(x) = x^2/(x+3)\) has the desired characteristics.

Step by step solution

01

Determine the Vertical Asymptote

A vertical asymptote occurs in a rational function where the denominator equals zero and the numerator does not. So, the denominator should be a factor that equals zero at \(x = -3\). A function that has this property is: \(x+3\). So, the denominator of the function is \(x+3\). F(x) can be written as: \(F(x) = N(x)/(x+3)\). Where \(N(x)\) is the numerator of the function.
02

Determine the Horizontal Asymptote

To not have a horizontal asymptote, the degree of the numerator of the function should be greater than the degree of the denominator. This way, as \(x \rightarrow \pm \infty\), the function will not approach any y-value. Let's choose the numerator to be a quadratic function, making its degree 2, which is higher than the degree of the denominator. Let's choose \(N(x) = x^2\). So, the function \(F(x) = x^2/(x+3)\) exhibits the desired characteristics.

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 a graphing utility to graph the function. Choose a window that allows all relative extrema and points of inflection to be identified on the graph. \(y=(1-x)^{2 / 3}\)

Find the differential \(d y\). \(y=\sqrt{9-x^{2}}\)

The cost and revenue functions for a product are \(C=25.5 x+1000\) and \(R=75.5 x\) (a) Find the average profit function \(\bar{P}=\frac{R-C}{x}\). (b) Find the average profits when \(x\) is 100,500 , and 1000 . (c) What is the limit of the average profit function as \(x\) approaches infinity? Explain your reasoning.

Sketch the graph of the function. Label the intercepts, relative extrema, points of inflection, and asymptotes. Then state the domain of the function. \(y=\frac{2 x}{x^{2}-1}\)

A manufacturer determines that the demand \(x\) for a product is inversely proportional to the square of the price \(p\). When the price is \(\$ 10\), the demand is 2500\. Find the revenue \(R\) as a function of \(x\) and approximate the change in revenue for a one-unit increase in sales when \(x=3000\). Make a sketch showing \(d R\) and \(\Delta R\).
See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation

Mechanics 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.