Domanda del libro di testo
In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x2+x−6)/(x−3)
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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 86
Solve each inequality in Exercises 86–91 using a graphing utility. x2 + 3x - 10 > 0
Guida verificata passo dopo passo1
Rewrite the inequality to understand the expression clearly: \(x^{2} + 3x - 10 > 0\).
Find the roots of the quadratic equation \(x^{2} + 3x - 10 = 0\) by using the quadratic formula: \(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\), where \(a=1\), \(b=3\), and \(c=-10\).
Calculate the discriminant \(\Delta = b^{2} - 4ac\) to determine the nature of the roots.
Use the roots found to divide the number line into intervals. Test a value from each interval in the inequality \(x^{2} + 3x - 10 > 0\) to determine where the inequality holds true.
Express the solution set as intervals where the quadratic expression is greater than zero, based on the test results from the intervals.
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Quadratic Inequalities
A quadratic inequality involves a quadratic expression set greater than or less than a value, often zero. Solving it means finding the range of x-values where the inequality holds true. This typically requires identifying where the quadratic expression is positive or negative.
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3:21
Nonlinear Inequalities
Graphing Quadratic Functions
Graphing a quadratic function y = ax² + bx + c helps visualize its shape (a parabola) and identify where it lies above or below the x-axis. The points where the graph crosses the x-axis (roots) divide the number line into intervals to test for the inequality.
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5:26Graphs of Logarithmic Functions
Using a Graphing Utility
A graphing utility is a tool or calculator that plots functions quickly and accurately. It helps find the roots of the quadratic and shows where the graph is above or below the x-axis, making it easier to determine the solution set for the inequality.
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5:31Graphing Rational Functions Using Transformations
Pratica correlata
Domanda del libro di testo
Exercises 82–84 will help you prepare for the material covered in the next section. Let f(x)=an(x4−3x2−4). If f(3)=−150, determine the value of a_n.
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Domanda del libro di testo
Solve each inequality in Exercises 86–91 using a graphing utility. 2x2 + 5x - 3 ≤ 0
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Domanda del libro di testo
In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x3+1)/(x2+2x)
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Domanda del libro di testo
In Exercises 81–88, a. Find the slant asymptote of the graph of each rational function and b. Follow the seven-step strategy and use the slant asymptote to graph each rational function. f(x)=(x2+1)/x
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Domanda del libro di testo
Solve each inequality in Exercises 86–91 using a graphing utility. x3 + x2 - 4x - 4 > 0
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