Skip to main content
Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 2 - Functions and GraphsProblema 43
Capitolo 3, Problema 43

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. (x − 3)² + (y + 1)² = 36

Guida verificata passo dopo passo
1
Recognize that the given equation is in the standard form of a circle: \(\left(x - h\right)^2 + \left(y - k\right)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius.
Identify the center \((h, k)\) by comparing the given equation \(\left(x - 3\right)^2 + \left(y + 1\right)^2 = 36\) to the standard form. Note that \(y + 1\) can be rewritten as \(y - (-1)\), so the center is at \((3, -1)\).
Determine the radius \(r\) by taking the square root of the right side of the equation: \(r = \sqrt{36}\).
To find the domain of the circle, consider the horizontal distance from the center. The domain is all \(x\) values such that \(x\) is between \(h - r\) and \(h + r\), or \(3 - r \leq x \leq 3 + r\).
To find the range of the circle, consider the vertical distance from the center. The range is all \(y\) values such that \(y\) is between \(k - r\) and \(k + r\), or \(-1 - r \leq y \leq -1 + r\).

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
2m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Equation of a Circle

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. This form helps identify the circle's position and size directly from the equation.
Video consigliato:
5:18
Circles in Standard Form

Domain and Range of a Circle

The domain and range of a circle are the sets of possible x and y values, respectively. For a circle centered at (h, k) with radius r, the domain is [h - r, h + r] and the range is [k - r, k + r], representing all points covered by the circle horizontally and vertically.
Video consigliato:
5:18
Circles in Standard Form

Graphing Circles

Graphing a circle involves plotting its center and using the radius to mark points in all directions. This visual representation helps confirm the circle's shape and aids in identifying the domain and range by observing the extent of the graph along the x- and y-axes.
Video consigliato:
5:18
Circles in Standard Form
Pratica correlata
Domanda del libro di testo

Give the slope and y-intercept of each line whose equation is given. Then graph the linear function. f(x) = (3/4)x-2

123
views
Domanda del libro di testo

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)², x ≤ 1

637
views
Domanda del libro di testo

Use the graph of y = f(x) to graph each function g. g(x) = (1/2)f(2x)

635
views
Domanda del libro di testo

Find f−g and determine the domain for each function. f(x)= = (5x+1)/(x² - 9), g(x) = (4x -2)/(x² - 9)

1196
views
Domanda del libro di testo

Find ƒ+g and determine the domain for each function.

f(x)= = (5x+1)/(x² - 9), g(x) = (4x -2)/(x² - 9)

914
views
Domanda del libro di testo

In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (4, -7) and parallel to the line whose equation is 3x + y - 9 = 0.

305
views