Skip to main content
Ch. 3 - Polynomial and Rational Functions
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 3 - Polynomial and Rational FunctionsProblema 48
Capitolo 4, Problema 48

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−3)/(x+2)≤0

Guida verificata passo dopo passo
1
Identify the rational inequality: \(\frac{-x - 3}{x + 2} \leq 0\).
Find the critical points by setting the numerator and denominator equal to zero separately: solve \(-x - 3 = 0\) and \(x + 2 = 0\).
Determine the critical points: from \(-x - 3 = 0\), solve for \(x\); from \(x + 2 = 0\), solve for \(x\). These points divide the number line into intervals.
Test each interval by choosing a test value from each interval and substituting it into the inequality \(\frac{-x - 3}{x + 2} \leq 0\) to check if the inequality holds.
Based on the test results, write the solution set in interval notation, remembering to exclude any points where the denominator is zero and include points where the expression equals zero if the inequality is non-strict (\(\leq\)).

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:
6m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Rational Inequalities

Rational inequalities involve expressions where one polynomial is divided by another, and the inequality compares this ratio to zero or another value. Solving them requires finding where the rational expression is positive, negative, or zero by analyzing the signs of numerator and denominator.
Video consigliato:
3:21
Nonlinear Inequalities

Critical Points and Sign Analysis

Critical points occur where the numerator or denominator equals zero, dividing the number line into intervals. By testing values in each interval, you determine the sign of the rational expression, which helps identify where the inequality holds true.
Video consigliato:
05:46
Point-Slope Form

Interval Notation and Graphing Solutions

After determining the solution intervals, express them using interval notation to clearly show the range of values satisfying the inequality. Graphing on a number line visually represents these intervals, indicating included or excluded points based on inequality symbols.
Video consigliato:
05:18
Interval Notation
Pratica correlata
Domanda del libro di testo

Write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 2x2 but with the given point as the vertex. (5, 3)

1049
views
Domanda del libro di testo

Give the domain and the range of each quadratic function whose graph is described. Maximum = -6 at x = 10

1089
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) + 2

721
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+1) − 2

789
views
Domanda del libro di testo

In Exercises 47–48, find an nth-degree polynomial function with real coefficients satisfying the given conditions. Verify the real zeros and the given function value. n = 3; 2 and 2 - 3i are zeros; f(1) = -10

1172
views
Domanda del libro di testo

Find all zeros of the polynomial function or solve the given polynomial equation. Use the Rational Zero Theorem, Descartes's Rule of Signs, and possibly the graph of the polynomial function shown by a graphing utility as an aid in obtaining the first zero or the first root. 4x4−x3+5x2−2x−6=0

762
views