Textbook Question
In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. [- 3, 1]
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- 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
Chapter 2, Problem 3a
Plot the given point in a rectangular coordinate system. (- 2, 3)
Verified step by step guidance1
Understand the rectangular coordinate system: It consists of two perpendicular axes, the x-axis (horizontal) and the y-axis (vertical), which intersect at the origin (0, 0). Points are represented as ordered pairs (x, y).
Identify the coordinates of the given point: The point (-2, 3) has an x-coordinate of -2 and a y-coordinate of 3.
Locate the x-coordinate: Start at the origin (0, 0) and move 2 units to the left along the x-axis because the x-coordinate is -2.
Locate the y-coordinate: From the position at x = -2, move 3 units up along the y-axis because the y-coordinate is 3.
Mark the point: Place a dot at the location where x = -2 and y = 3. This is the graphical representation of the point (-2, 3) in the rectangular coordinate system.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Rectangular Coordinate System
A rectangular coordinate system, also known as the Cartesian coordinate system, consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Each point in this system is defined by an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. This system allows for the precise location of points in a two-dimensional space.
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Plotting Points
Plotting points involves marking a specific location on the coordinate plane based on its coordinates. For the point (-2, 3), the x-coordinate is -2, which means you move 2 units left from the origin along the x-axis, and the y-coordinate is 3, indicating you move 3 units up along the y-axis. The intersection of these movements gives the exact location of the point.
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Ordered Pairs
An ordered pair is a pair of numbers used to represent a point in a coordinate system, written in the form (x, y). The first number, 'x', corresponds to the horizontal position, while the second number, 'y', corresponds to the vertical position. The order of the numbers is crucial, as switching them would represent a different point in the coordinate plane.
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Related Practice
Textbook Question
Solve each equation in Exercises 1 - 14 by factoring.
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Textbook Question
In Exercises 1–8, add or subtract as indicated and write the result in standard form. (3 + 2i) - (5 - 7i)
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Textbook Question
In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. [- 5, 2)
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Textbook Question
Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle.
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Textbook Question
Graph each equation in Exercises 1–4. Let x= -3, -2. -1, 0, 1, 2 and 3. y = |x|-2
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