Domanda del libro di testo
Determine which functions are polynomial functions. For those that are, identify the degree.
929
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 9
Use the graph of the rational function in the figure shown to complete each statement in Exercises 9–14.
As , ____
Guida verificata passo dopo passo1
Identify the point of interest on the x-axis, which is \(x \to -3^-\), meaning we are approaching \(-3\) from the left side.
Look at the graph near \(x = -3\) on the left side to observe the behavior of the function \(f(x)\) as \(x\) approaches \(-3\) from values less than \(-3\).
Notice the value of \(f(x)\) as \(x\) gets closer to \(-3\) from the left. Check if the function values increase without bound (go to \(+\infty\)), decrease without bound (go to \(-\infty\)), or approach a finite number.
From the graph, observe that as \(x\) approaches \(-3\) from the left, the function \(f(x)\) decreases without bound, meaning \(f(x) \to -\infty\).
Summarize the behavior: As \(x \to -3^-\), \(f(x) \to -\infty\).
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.
Vertical Asymptotes
Vertical asymptotes occur where the function approaches infinity or negative infinity as the input approaches a specific value. They indicate values of x where the function is undefined, often due to division by zero in rational functions. In the graph, vertical asymptotes are shown at x = 6 and x = 14.
Video consigliato:
3:12
Determining Vertical Asymptotes
Horizontal Asymptotes
A horizontal asymptote represents the value that the function approaches as x tends to positive or negative infinity. It shows the end behavior of the function. In this graph, the horizontal asymptote is y = 0, meaning the function values get closer to zero as x becomes very large or very small.
Video consigliato:
4:48Determining Horizontal Asymptotes
Limit Behavior Near a Point
The limit of a function as x approaches a specific value from the left or right describes the function's behavior near that point. For example, as x approaches -3 from the left (x → -3⁻), the function value approaches a certain number or infinity. Understanding this helps in interpreting the graph and completing limit statements.
Video consigliato:
05:01Identifying Intervals of Unknown Behavior
Pratica correlata
Domanda del libro di testo
Among all pairs of numbers whose difference is 14, find a pair whose product is as small as possible. What is the minimum product?
1380
views
1
comments
Domanda del libro di testo
In Exercises 9–16, a) List all possible rational zeros. b) Use synthetic division to test the possible rational zeros and find an actual zero. c) Use the quotient from part (b) to find the remaining zeros of the polynomial function. f(x)=x3+x2−4x−4
711
views
Domanda del libro di testo
Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x)=2(x−3)2+1
1116
views
Domanda del libro di testo
Use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).]
a.b. c. d.
1202
views
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 jointly as a and b and inversely as the square root of c. y = 12 when a = 3, b = 2, and c = 25. Find y when a = 5, b = 3 and c = 9.
644
views