Precalculus (6th Edition) Blitzer

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

Chapter 2 - Mid-Chapter Check Point - Page 381: 8


The domain and range of the function are $\left( -\infty ,\infty \right)$ and $\left[ -4,\infty \right)$ respectively.

Work Step by Step

The graph is a parabola. Now, since $f\left( x \right)$ is a polynomial, it exists for every value of $x$ on the real axis. Therefore, the domain of $f\left( x \right)={{\left( x-3 \right)}^{2}}-4$ is $\left( -\infty ,\infty \right)$. Also since, $\begin{align} & {{\left( x-3 \right)}^{2}}\ge 0 \\ & {{\left( x-3 \right)}^{2}}-4\ge -4 \\ & f\left( x \right)\ge -4 \\ & f\left( x \right)\in \left[ -4,\infty \right) \\ \end{align}$ So, the range of the function is $\left[ -4,\infty \right)$.
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