Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Review - Exercises - Page 135: 117

Answer

$(a)$ Symmetry with respect to the origin $(b)$ $x$-intercept $A(0,1)$ and $B(0,-1)$ $y$-intercept $C(-1,0)$ and $D(1,0)$

Work Step by Step

$(a)$ As we can see from the image of the graph above, it is symmetrical with respect to the origin. Algebraically, if we replace $x$ by $-x$ and $y$ by $-y$ equation will be still equivalent to the original one. $(b)$ $x$-intercept happens when $y=0$ $x^2+4x\times0+0^2=1$ $x^2=1$ $x=±1$ $A(0,1)$ and $B(0,-1)$ $y$-intercept happens when $x=0$ $0^2+4y\times0+y^2=1$ $y^2=1$ $y=±1$ $C(-1,0)$ and $D(1,0)$
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