Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.9 - Distance and Midpoint Formulas; Circles - Exercise Set - Page 280: 41


Center: $(0, 0)$ Radius = 4 Domain: $[-4, 4]$ RangeL $[-4, 4]$ Refer to the image below for the graph.

Work Step by Step

RECALL: The standard equation of a circle whose center is at $(h, k)$ and has a radius of $r$ units is: $(x-h)^2 + (y-k)^2 = r^2$ Thus, using the standard form given above as guide, the given circle has: Center: $(0, 0)$ Radius = $\sqrt{16} = 4$ To graph the circle, perform the following steps: (1) Plot the center $(0, 0)$. (2) From the center, plot the points 4 units to the center’s left, right, above, and below. These points are $(-4, 0)$, $(4, 0)$, $(0, 4)$, and $(0, -4)$, respectively. Connect these points using a curve to form a circle. The domain is the set of x-values covered by the graph. Since the graph covers the x-values from -4 to 4, then the domain is: $[-4, 4]$ The range is the set of y-values covered by the graph. Since the graph covers the y-values from -4 to 4, then the range is: $[-4, 4]$
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