Precalculus (6th Edition) Blitzer

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

Chapter 2 - Section 2.2 - Quadratic Functions - Exercise Set - Page 330: 45


The Domain of the function is $\left( -\infty ,\infty \right)$ and its Range is $\left[ -2,\infty \right)$.

Work Step by Step

We have to find the range of the function: we use the vertex of the parabola, which is $\left( -1,-2 \right)$. Since the parabola open upwards, the minimum value of the function is given by the y-coordinate of the vertex. Thus, the minimum value is $-2$. The maximum value of the function would be $\infty $. Thus, the range of the function is $\left( -2,\infty \right)$. For the domain, see the values of the function at which the function is defined. The function is defined at all real values. Thus, the domain of the function is $\left( -\infty ,\infty \right)$. Thus, the range of the function is $\left( -2,\infty \right)$ and its domain is $\left( -\infty ,\infty \right)$.
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