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Begin by graphing the standard cubic function, f(x) = x³. Then use transformations of this graph to graph the given function. r(x) = (x − 2)³ +1
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Ch. 2 - Functions and Graphs
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 3, Problema 104
Exercises 103–105 will help you prepare for the material covered in the next section. Use a rectangular coordinate system to graph the circle with center (1, -1) and radius 1.
Guida verificata passo dopo passo1
Recall the standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is given by:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
Identify the center \((h, k)\) and radius \(r\) from the problem: here, \(h = 1\), \(k = -1\), and \(r = 1\).
Substitute these values into the standard form equation to write the specific equation of the circle:
\[ (x - 1)^2 + (y + 1)^2 = 1^2 \]
To graph the circle, first plot the center point at \((1, -1)\) on the rectangular coordinate system.
From the center, use the radius to mark points 1 unit away in all four directions (up, down, left, right), then sketch the circle passing through these points.
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Equation of a Circle
The equation of a circle with center (h, k) and radius r is given by (x - h)² + (y - k)² = r². This formula represents all points (x, y) that are exactly r units away from the center. Understanding this equation is essential for graphing the circle accurately.
Video consigliato:
5:18
Circles in Standard Form
Coordinate Plane and Plotting Points
A rectangular coordinate system consists of an x-axis and y-axis intersecting at the origin. Plotting points involves locating coordinates (x, y) on this plane. Knowing how to plot the center and points on the circle helps visualize and draw the circle correctly.
Video consigliato:
05:10Graphs & the Rectangular Coordinate System
Radius and Distance in the Plane
The radius is the fixed distance from the center of the circle to any point on its circumference. Understanding how to measure and use this distance in the coordinate plane allows you to determine points on the circle by moving r units horizontally or vertically from the center.
Video consigliato:
5:12Graph Ellipses at Origin
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Exercises 103–105 will help you prepare for the material covered in the next section. Let (x1, y₁) = (7, 2) and (x2, y2) = (1, −1). Find √[(x2 − x1)² + (y2 − y₁)²]. Express the - answer in simplified radical form.
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