Domanda del libro di testo
Use synthetic division to show that 5 is a solution of x^4−4x^3−9x^2+16x+20=0. Then solve the polynomial equation.
676
views
Ch. 3 - Polynomial and Rational Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Non è quello che usi tu?Cambia libro di testoScegli un libro di testo diverso
TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 4, Problema 79
In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(3x2+x−4)/(2x2−5x)
Guida verificata passo dopo passo1
Identify the domain of the function by finding the values of that make the denominator zero. Solve to find these values, since the function is undefined there.
Find the intercepts: For the y-intercept, evaluate if it is in the domain. For the x-intercepts, set the numerator equal to zero and solve to find the values of where .
Determine any vertical asymptotes by using the values of that make the denominator zero (from step 1), provided these values do not also make the numerator zero (which would indicate a hole instead).
Find the horizontal or oblique (slant) asymptote by comparing the degrees of the numerator and denominator polynomials. Since both are degree 2, divide the leading coefficients to find the horizontal asymptote.
Analyze the behavior of the function near the vertical asymptotes and at the ends of the domain by testing values of in each interval determined by the vertical asymptotes, and use this information to sketch the graph.
Risposta video verificata per un problema simile:
Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
17mConcetti chiave
Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.
Rational Functions
A rational function is a ratio of two polynomials, expressed as f(x) = P(x)/Q(x). Understanding its domain, where the denominator Q(x) ≠ 0, is essential to avoid undefined values and to analyze the function's behavior.
Video consigliato:
6:04
Intro to Rational Functions
Asymptotes
Asymptotes are lines that the graph of a function approaches but never touches. Vertical asymptotes occur where the denominator is zero, and horizontal or oblique asymptotes describe end behavior as x approaches infinity or negative infinity.
Video consigliato:
6:24Introduction to Asymptotes
Graphing Steps for Rational Functions
Graphing rational functions involves identifying domain restrictions, intercepts, asymptotes, and behavior near asymptotes, then plotting points to sketch the curve. Following a systematic approach ensures an accurate and complete graph.
Video consigliato:
8:19How to Graph Rational Functions
Pratica correlata
Domanda del libro di testo
Solve the variation problems in Exercises 77–82. The distance that a body falls from rest is directly proportional to the square of the time of the fall. If skydivers fall 144 feet in 3 seconds, how far will they fall in 10 seconds?
593
views
Domanda del libro di testo
Solve the variation problems in Exercises 77–82. The pitch of a musical tone varies inversely as its wavelength. A tone has a pitch of 660 vibrations per second and a wavelength of 1.6 feet. What is the pitch of a tone that has a wavelength of 2.4 feet?
579
views
Domanda del libro di testo
In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x2−1)/x
648
views
Domanda del libro di testo
Find the inverse of f(x)=(x−10)/(x+10).
559
views
Domanda del libro di testo
Exercises 82–84 will help you prepare for the material covered in the next section. Solve: x2+4x−1=0
474
views