Domanda del libro di testo
In Exercises 17–24, a) List all possible rational roots. b) List all possible rational roots. c) Use the quotient from part (b) to find the remaining roots and solve the equation. 6x3+25x2−24x+5=0
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Ch. 3 - Polynomial and Rational Functions
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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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 21
Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function.
Guida verificata passo dopo passo1
Identify the leading term of the polynomial function. The leading term is the term with the highest power of \(x\). In this case, it is \$5x^4$.
Determine the degree of the polynomial, which is the exponent of the leading term. Here, the degree is 4, which is an even number.
Look at the leading coefficient, which is the coefficient of the leading term. Here, the leading coefficient is 5, a positive number.
Apply the Leading Coefficient Test: For an even degree polynomial with a positive leading coefficient, the end behavior is such that as \(x \to \infty\), \(f(x) \to \infty\), and as \(x \to -\infty\), \(f(x) \to \infty\).
Summarize the end behavior based on the test: both ends of the graph will rise upwards toward positive infinity.
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Leading Coefficient Test
The Leading Coefficient Test uses the degree and leading coefficient of a polynomial to determine its end behavior. It states that the sign of the leading coefficient and whether the degree is even or odd dictate how the graph behaves as x approaches positive or negative infinity.
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06:08
End Behavior of Polynomial Functions
Degree of a Polynomial
The degree of a polynomial is the highest power of the variable in the expression. It influences the shape and end behavior of the graph. For example, even-degree polynomials have similar end behaviors on both sides, while odd-degree polynomials have opposite end behaviors.
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05:16Standard Form of Polynomials
End Behavior of Polynomial Functions
End behavior describes how the values of a polynomial function behave as x approaches positive or negative infinity. It helps predict whether the graph rises or falls on the far left and right sides, based on the leading term's degree and coefficient.
Video consigliato:
06:08End Behavior of Polynomial Functions
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