Answered: Determine whether the graph of the…

Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter8: Introduction To Functions

Section8.2: Points, Lines, And Their Graphs

Problem 27OE

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Question

Determine whether the graph of the given equation is symmetric with respect to the y-axis, the x-axis, the origin, more than one of these, or none of these. x³ - y² = 5

Expert Solution

Step 1

Solution:- The graph is

$x^{3} - y^{2} = 5$

we have to test either the graph is symmetrical about y-axis, x-axis the origin, more than one of these, or none of these.

Step 2

$x^{3} - y^{2} = 5 . . . . . . . . . . (1) a) f o r x - a x i s s y m m e t r y . r e p l a c e y = - y w e w e g e t x^{3} - {(- y)}^{2} = 5 x^{3} - y^{2} = 5 w h i c h i s e q u i v a l e n t t o (1) s o t h a t g r a p h i s s y m m e t r i c a l a b o u t x - a x i s .$

$b) f o r y - a x i s s y m m e t r y . r e p l a c e x = - x w e w e g e t {(- x)}^{3} - y^{2} = 5 - x^{3} - y^{2} = 5 w h i c h i s n o t e q u i v a l e n t t o (1) s o t h a t g r a p h i s n o t s y m m e t r i c a l a b o u t y - a x i s .$

$c) a b o u t o r i g i n . r e p l a c e x = - x a n d y = - y w e w i l l g e t {(- x)}^{3} - {(- y)}^{2} = 5 - x^{3} - y^{2} = 5 w h i c h i s n o t e q u i v a l e n t t o e q (1) s o g r a p h i s n o t s y m m e t r i c a l a b o u t o r i g i n .$

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