Domanda del libro di testo
Graph each equation in a rectangular coordinate system. y = -2
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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 49
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
Guida verificata passo dopo passo1
Step 1: Recognize the standard form of a circle's equation, which is (x − h)² + (y − k)² = r², where (h, k) is the center of the circle and r is the radius.
Step 2: Compare the given equation x² + (y − 1)² = 1 to the standard form. Notice that h = 0 (since x² is the same as (x − 0)²), k = 1 (from (y − 1)²), and r² = 1.
Step 3: Determine the center of the circle. From the comparison, the center is (h, k) = (0, 1).
Step 4: Find the radius of the circle. Since r² = 1, take the square root of both sides to find r = √1 = 1.
Step 5: To graph the circle, plot the center at (0, 1) and draw a circle with a radius of 1. The domain of the circle is the set of x-values from -1 to 1, and the range is the set of y-values from 0 to 2.
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Circle Equation
The standard form of a circle's equation is (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. In the given equation, x² + (y - 1)² = 1, we can identify the center as (0, 1) and the radius as 1, since r² = 1.
Video consigliato:
5:18
Circles in Standard Form
Graphing Circles
To graph a circle, plot the center point and use the radius to mark points in all directions (up, down, left, right) from the center. The resulting shape is a circle, and understanding how to accurately represent this visually is crucial for analyzing the relation's domain and range.
Video consigliato:
5:18Circles in Standard Form
Domain and Range
The domain of a relation refers to all possible x-values, while the range refers to all possible y-values. For the circle described, the domain is [-1, 1] and the range is [0, 2], as these intervals encompass all x and y coordinates that the circle can reach based on its center and radius.
Video consigliato:
4:22Domain & Range of Transformed Functions
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