Skip to main content
Ch. 2 - Functions and Graphs
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 2 - Functions and GraphsProblem 45
Chapter 3, Problem 45

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 - 2)² = 4

Verified step by step guidance
1
Identify the given equation of the circle: \( (x+3)^2 + (y+2)^2 = 4 \). This is in the standard form of a circle's equation: \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h, k) \) is the center and \( r \) is the radius.
Compare the given equation to the standard form to find the center. Since the equation is \( (x + 3)^2 + (y + 2)^2 = 4 \), rewrite it as \( (x - (-3))^2 + (y - (-2))^2 = 2^2 \). Therefore, the center is at \( (-3, -2) \).
Determine the radius by taking the square root of the right side of the equation. Here, \( r^2 = 4 \), so \( r = 2 \).
To graph the circle, plot the center at \( (-3, -2) \) on the coordinate plane. Then, draw a circle with radius 2 units around this center, marking points 2 units away in all directions (up, down, left, right).
Identify the domain and range from the graph or equation. The domain is all \( x \)-values covered by the circle, which is from \( h - r \) to \( h + r \), so from \( -3 - 2 \) to \( -3 + 2 \). The range is all \( y \)-values covered by the circle, from \( k - r \) to \( k + r \), so from \( -2 - 2 \) to \( -2 + 2 \).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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. By comparing the given equation to this form, you can identify the circle's center and radius directly.
Recommended video:
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 in understanding the shape and position of the circle on the coordinate plane.
Recommended video:
5:18
Circles in Standard Form

Domain and Range of a Circle

The domain of a circle is the set of all x-values covered by the circle, and the range is the set of all y-values. These can be found by considering the center coordinates and radius, as the circle extends r units horizontally and vertically from the center.
Recommended video:
5:18
Circles in Standard Form
Related Practice
Textbook Question

In Exercises 39–50, graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = x², g(x) = x² - 2

Textbook Question

Find ƒ+g and determine the domain for each function. f(x)= = 8x/(x - 2), g(x) = 6/(x+3)

Textbook Question

Graph the given functions, f and g, in the same rectangular coordinate system. Select integers for x, starting with -2 and ending with 2. Once you have obtained your graphs, describe how the graph of g is related to the graph of f. f(x) = |x|, g(x) = |x| − 2

Textbook Question

Find ƒ+g, f−g, fg, and f/g. Determine the domain for each function. f(x)= = (3x+1)/(x² - 25), g(x) = (2x -4)/(x² - 25)

3
views
Textbook Question

After a 30% price reduction, you purchase a 50″ 4K UHD TV for \$245. What was the television's price before the reduction?

1
views
Textbook Question

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