1. Lial/Hungerford/Holcomb/Mullins: Mathematics with Applications 11e Finite Mathematics with Applications 11e
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2. Graphs, Lines and Inequalities
Chapter 2
Graphs, Lines and Inequalities
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Section 2.1
Graphs
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Example:
Sketch the graph of
Solution:
Since we cannot plot infinitely many points, we construct a table of y-values for a reasonable number of x-values, plot the corresponding points, and make an “educated guess” about the rest.
The table above shows a few x-values and y-values.
Sketch the line that connects the points.
The graph above shows the points on the coordinate plane. The points indicate that the graph should be a straight line.
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Section 2.2
Equations of Lines
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24. Find the slope of the line through the points
Example:
Find the slope of the line through the points
Solution:
Let Use the definition of slope as follows:
The slope can also be found by letting
In that case,
which is the same answer.
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Section 2.3
Linear Models
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Example:
Social Science Two linear models were constructed from data on the number of full-time faculty at four-year colleges and universities: For each model, determine the five residuals, square of each residual, and the sum of the squares of the residual.
Solution:
The information for the first model is summarized in the following table:
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Example:
Social Science Two linear models were constructed from data on the number of full-time faculty at four-year colleges and universities: For each model, determine the five residuals, square of each residual, and the sum of the squares of the residual.
Solution:
The information for the second model is summarized in the following table:
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Example:
Social Science Two linear models were constructed from data on the number of full-time faculty at four-year colleges and universities: For each model, determine the five residuals, square of each residual, and the sum of the squares of the residual.
Solution:
Compare the two models by looking at their squared residuals.
According to this measure of the error, the line is a better fit for the data because the sum of the squares of its residuals is smaller than the sum of the squares of the residuals for
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Section 2.4
Linear Inequalities
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Example:
Solve
Solution:
Add to both sides.
Add to both sides.
To finish solving the inequality, multiply both sides by Since is negative, change the direction of the inequality symbol:
The solution set, , is graphed below. The bracket indicates that is included in the solution.
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78. Polynomial and Rational Inequalities
Section 2.5
Polynomial and Rational Inequalities
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79. Use the graph of below to solve the inequality
Example:
Use the graph of below to solve the inequality
Solution:
Each point on the graph has coordinates of the form The number x is a solution of the inequality exactly when the second coordinate of this point is positive—that is, when the point lies above the x-axis.
The solution of the inequality can be determined from the graph by noting the x-values for which the curve is above the x-axis.
and when
The graph is above the x-axis when
So the solutions of the inequality are all numbers x in the interval or the interval
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