Precalculus (6th Edition) Blitzer

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

Chapter 4 - Section 4.1 - Angles and Radian Measure - Exercise Set - Page 534: 128

Answer

The domain of ${{x}^{2}}+{{y}^{2}}=1$ is $\left[ -1,1 \right]$ and its range is $\left[ -1,1 \right]$.

Work Step by Step

Consider the provided equation: ${{x}^{2}}+{{y}^{2}}=1$ The provided equation can also be written as: ${{\left( x-0 \right)}^{2}}+{{\left( y-0 \right)}^{2}}={{\left( 1 \right)}^{2}}$ Now, this represents the standard equation of a circle with its center at $\left( 0,0 \right)$ and radius of $1$ unit. For the domain: The domain of a function means "all the possible values of x in the function". Here in the graph, note that the values of x range between $-1$ and $1$, including these values. So, the domain of the relation is $\left[ -1,1 \right]$ For the range: The range of a function means "all the possible values of y in the function". Here in the graph, note that the values of y range between $-1$ and $1$ including these values. So, the range of the relation is $\left[ -1,1 \right]$ Therefore, the domain and range of the function are $\left[ -1,1 \right]$ and $\left[ -1,1 \right]$ respectively.
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