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 87
Solve each inequality in Exercises 86–91 using a graphing utility. 2x2 + 5x - 3 ≤ 0
Guida verificata passo dopo passo1
Identify the inequality to solve: \(2x^{2} + 5x - 3 \leq 0\).
Rewrite the inequality as an equation to find critical points: \(2x^{2} + 5x - 3 = 0\).
Use the quadratic formula to solve for \(x\): \(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\), where \(a=2\), \(b=5\), and \(c=-3\).
Calculate the roots from the quadratic formula; these roots divide the number line into intervals to test for the inequality.
Use a graphing utility to plot \(y = 2x^{2} + 5x - 3\) and determine where the graph lies on or below the \(x\)-axis (i.e., where \(y \leq 0\)) to find the solution intervals.
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Quadratic Inequalities
A quadratic inequality involves a quadratic expression set less than, greater than, or equal to zero. Solving it requires finding the range of x-values where the quadratic expression satisfies the inequality, often by analyzing the parabola's position relative to the x-axis.
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3:21
Nonlinear Inequalities
Graphing Quadratic Functions
Graphing a quadratic function y = ax² + bx + c produces a parabola. The graph helps visualize where the function is above or below the x-axis, which corresponds to positive or negative values of the quadratic expression, aiding in solving inequalities.
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5:26Graphs of Logarithmic Functions
Using Graphing Utilities
Graphing utilities, such as graphing calculators or software, allow quick plotting of functions to identify roots and intervals where inequalities hold. They provide a visual method to solve quadratic inequalities by showing where the graph lies relative to the x-axis.
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5:31Graphing Rational Functions Using Transformations
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