Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 5 - Exponential and Logarithmic Functions - 5.3 Exponential Functions - 5.3 Assess Your Understanding - Page 285: 139

Answer

(a) See graph. (b) $(-\infty,\infty)$, $[-4,\infty)$. (c) increasing $(-1,\infty)$, decreasing $(-\infty,-1)$.

Work Step by Step

(a) Given $f(x)=x^2+2x-3=(x+1)^2-4$, we have $a=1\gt0$, thus the graph opens up with vertex $(-1,-4)$, axis of symmetry $x=-1$, y-intercept $f(0)=-3$ and x-intercept(s) $x=-1\pm2=-3,1$. See graph. (b) Based on the graph, we can identify the domain as $(-\infty,\infty)$ and range as $[-4,\infty)$. (c) Based on the graph, we can find that $f$ is increasing on $(-1,\infty)$ and decreasing on $(-\infty,-1)$.
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