Domanda del libro di testo
Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x + 1)/(x + 3) < 2
520
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 57
Follow the seven steps to graph each rational function. f(x)=4x/(x−2)
Guida verificata passo dopo passo1
Identify the domain of the function by determining the values of \(x\) that make the denominator zero. For \(f(x) = \frac{4x}{x - 2}\), set the denominator equal to zero: \(x - 2 = 0\) and solve for \(x\).
Find the vertical asymptote(s) by using the values of \(x\) that are excluded from the domain. These occur where the denominator is zero, so the vertical asymptote is at \(x = 2\).
Determine the horizontal asymptote by comparing the degrees of the numerator and denominator. Since both numerator and denominator are degree 1, divide the leading coefficients to find the horizontal asymptote: \(y = \frac{4}{1} = 4\).
Calculate the \(x\)-intercept(s) by setting the numerator equal to zero and solving for \(x\). For \(4x = 0\), solve for \(x\) to find the \(x\)-intercept.
Calculate the \(y\)-intercept by evaluating \(f(0)\). Substitute \(x = 0\) into the function to find the corresponding \(y\)-value.
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:
5mConcetti 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), where Q(x) ≠ 0. Understanding the form helps identify domain restrictions and behavior, such as vertical asymptotes where the denominator is zero.
Video consigliato:
6:04
Intro to Rational Functions
Asymptotes of Rational Functions
Asymptotes are lines that the graph 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 involves identifying domain restrictions, intercepts, asymptotes, and plotting points to understand the function's shape. Following systematic steps ensures an accurate sketch of the function's behavior across its domain.
Video consigliato:
8:19How to Graph Rational Functions
Pratica correlata
Domanda del libro di testo
In Exercises 57–64, find the vertical asymptotes, if any, the horizontal asymptote, if one exists, and the slant asymptote, if there is one, of the graph of each rational function. Then graph the rational function. f(x) = 2x/(x^2 - 9)
702
views
Domanda del libro di testo
Exercises 53–60 show incomplete graphs of given polynomial functions. a) Find all the zeros of each function. b) Without using a graphing utility, draw a complete graph of the function. f(x)=2x4−3x3−7x2−8x+6
427
views
Domanda del libro di testo
Solve each rational inequality in Exercises 43–60 and graph the solution set on a real number line. Express each solution set in interval notation. (x + 4)/(2x - 1) ≤ 3
492
views
Domanda del libro di testo
Use transformations of f(x) = (1/x) or f(x) = (1/x2) to graph each rational function. g(x) = 1/(x + 2)2 - 1
1039
views
Domanda del libro di testo
Use transformations of f(x)=1/x or f(x)=1/x2 to graph each rational function. h(x)=1/(x−3)2+1
678
views