College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.2 - Graphs of Functions - 2.2 Exercises - Page 205: 78


$f(x)=-\sqrt{9−x^2}, -3\leq x\leq 3$

Work Step by Step

We are given $y=x^2+y^2=9=3^2$ This describes a circle with radius 3 centered at (0,0). We solve for y: $y^2=9−x^2$ $y=\pm\sqrt{9−x^2}$ We want the bottom half of the circle, so we take the negative: $y=-\sqrt{9−x^2}$ Thus the function is: $f(x)=-\sqrt{9−x^2}, -3\leq x\leq 3$
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