Textbook Question
Use the graph of y = f(x) to graph each function g. g(x) = -f(x + 1) − 1
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Ch. 2 - Functions and Graphs
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 3, Problem 49
Graph each equation in a rectangular coordinate system. y = -2
Verified step by step guidance1
Identify the type of equation given. The equation \(y = -2\) represents a horizontal line because \(y\) is constant for all values of \(x\).
Understand that for any value of \(x\), the value of \(y\) will always be \(-2\). This means the line is parallel to the \(x\)-axis.
To graph the line, plot several points where \(y = -2\). For example, points like \((0, -2)\), \((1, -2)\), and \((-1, -2)\) all lie on the line.
Draw a straight horizontal line through all these points extending across the coordinate plane.
Label the line with its equation \(y = -2\) to clearly indicate which line you have graphed.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Graphing Horizontal Lines
A horizontal line in the coordinate plane has the same y-value for all x-values. The equation y = -2 represents a horizontal line crossing the y-axis at -2, meaning every point on the line has y-coordinate -2 regardless of x.
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Graphing Lines in Slope-Intercept Form
Rectangular Coordinate System
The rectangular coordinate system consists of two perpendicular axes: the x-axis (horizontal) and the y-axis (vertical). Points are located using ordered pairs (x, y), where x is the horizontal position and y is the vertical position.
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05:10Graphs & the Rectangular Coordinate System
Plotting Points from an Equation
To graph an equation, identify points that satisfy it by substituting values for variables. For y = -2, choose any x-values and plot points with y fixed at -2, then connect these points to form the line.
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04:29Graphing Equations of Two Variables by Plotting Points
Related Practice
Textbook Question
In Exercises 39-52, a. Find an equation for ƒ¯¹(x). b. Graph ƒ and ƒ¯¹(x) in the same rectangular coordinate system. c. Use interval notation to give the domain and the range off and ƒ¯¹. f(x) = √(x-1)
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Textbook Question
In Exercises 41–52, give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. x² + (y − 1)² = 1
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Textbook Question
In Exercises 46–49, give the slope and y-intercept of each line whose equation is given. Then graph the line. 2x + 3y + 6 = 0
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Textbook Question
In Exercises 31–50, find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)
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Textbook Question
Find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x) = √(x -2), g(x) = √(2-x)
1241
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