Domanda del libro di testo
Solve each polynomial inequality in Exercises 1–42 and graph the solution set on a real number line. Express each solution set in interval notation. (x−4)(x+2)>0
553
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 1
Find the domain of each rational function. f(x)=5x/(x−4)
Guida verificata passo dopo passo1
Identify the rational function given: \(f(x) = \frac{5x}{x - 4}\).
Recall that the domain of a rational function includes all real numbers except where the denominator is zero, because division by zero is undefined.
Set the denominator equal to zero to find the values to exclude: \(x - 4 = 0\).
Solve the equation for \(x\): \(x = 4\).
Conclude that the domain of \(f(x)\) is all real numbers except \(x = 4\), which can be written in interval notation as \((-\infty, 4) \cup (4, \infty)\).
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:
1mConcetti 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 rational functions involves recognizing that the function is undefined where the denominator Q(x) equals zero, which affects the domain.
Video consigliato:
6:04
Intro to Rational Functions
Domain of a Function
The domain of a function is the set of all input values (x-values) for which the function is defined. For rational functions, the domain excludes values that make the denominator zero, since division by zero is undefined.
Video consigliato:
3:51Domain Restrictions of Composed Functions
Finding Values that Make the Denominator Zero
To find the domain of a rational function, set the denominator equal to zero and solve for x. These values are excluded from the domain because they cause division by zero, which is undefined in mathematics.
Video consigliato:
03:42Finding Zeros & Their Multiplicity
Pratica correlata
Domanda del libro di testo
Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies directly as x. y = 65 when x = 5. Find y when x = 12.
172
views
Domanda del libro di testo
Determine which functions are polynomial functions. For those that are, identify the degree.
1260
views
Domanda del libro di testo
Divide using long division. State the quotient, and the remainder, r(x). (x2+8x+15)÷(x+5)
1275
views
Domanda del libro di testo
The graph of a quadratic function is given. Write the function's equation, selecting from the following options.
1526
views
Domanda del libro di testo
In Exercises 1–4, use the vertex and intercepts to sketch the graph of each quadratic function. Give the equation for the parabola's axis of symmetry. Use the graph to determine the function's domain and range.
1109
views