Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 1 - Review - Concept Check - Page 133: 33

Answer

A) (i) The x axis (a, -b) This means that you take the equation and subistitute all y with (-) if after solving it, is the same as the original it means it is symmetric. (ii) y axis (-a,b) this means that you take the equation and subtitute all x with (-). If after solving it, is the same as the original it means it is symmetric. (iii) origin (-a,-b) this means that you take the equation and substitite all x and y by (-). If after solving it, is the same as the original it means it is symmetric B) x-axis symmetry.

Work Step by Step

A) How do you test whether the graph pf an equation is symmetric with respect to the (i) x axis (ii) y axs and (iii) origin? (i) The x axis (a, -b) This means that you take the equation and subistitute all y with (-) if after solving it, is the same as the original it means it is symmetric. (ii) y axis (-a,b) this means that you take the equation and subtitute all x with (-). If after solving it, is the same as the original it means it is symmetric. (iii) origin (-a,-b) this means that you take the equation and substitite all x and y by (-). If after solving it, is the same as the original it means it is symmetric. B) What type of symmetry does the graph of the equation $xy^{2}+y^{2}x^{2}=3x$ have? X axis $$x(-y)^{2}+(-y)^{2}x^{2}=3x$$ $$xy^{2}+y^{2}x^{2}=3x$$ It is symmetric respecting x axis. Y axis $$(-x)y^{2}+y^{2}(-x)^{2}=3(-x)$$ $$-xy^{2}+y^{2}x^{2}=-3x$$ No symmetry. Origin $$(-x)(-y)^{2}+(-y)^{2}(-x)^{2}=3(-x)$$ $$(-x)y^{2}+y^{2}x^{2}=-3x$$ No symmetry.
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