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For the given equation, list the intercepts and test for symmetry.  Y= -6x/x^2+81

Question

For the given equation, list the intercepts and test for symmetry. 

 

Y= -6x/x^2+81

check_circleAnswer
Step 1

Refer to the question,

To find the x and y intercepts put y=0 for x intercept and x=0 for y intercept.

Then,

-6x
Y =
r81
For x -intercept, put y
0
-6x
0=
x281
For y -intercept, put x 0
y=6(0)
(0)81
Y 0
So bothx and y intercepts are at the origin,(0,0)
help_outline

Image Transcriptionclose

-6x Y = r81 For x -intercept, put y 0 -6x 0= x281 For y -intercept, put x 0 y=6(0) (0)81 Y 0 So bothx and y intercepts are at the origin,(0,0)

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Step 2

Now to check for symmetry, a function is symmetric with respect to the x axis if f(a)=-f(a).

That is,

-6x
Y =-
81
f(x)(x) for symmetric about x axis
-6x
-6x
x81
x81
It is not symmetric about x axis
help_outline

Image Transcriptionclose

-6x Y =- 81 f(x)(x) for symmetric about x axis -6x -6x x81 x81 It is not symmetric about x axis

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Step 3

Then check symmetry about y axis, a function is symme...

-6x
Y =-
r81
f (x)
x) for symmetric about y axis
-6(-x)
(-x) +81
-6x
x81
6x
x281
It is not symmetric about y axis.
help_outline

Image Transcriptionclose

-6x Y =- r81 f (x) x) for symmetric about y axis -6(-x) (-x) +81 -6x x81 6x x281 It is not symmetric about y axis.

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Tagged in

Math

Algebra

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