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Which characteristic is correct for the function f(x)=−3x^4+7x^2 ?

 

 

  • neither even nor odd
  • both even and odd
  • even
  • odd
 Feb 6, 2018
 #1
avatar+102392 
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f(x)  =  -3(x)^4  + 7x^2

 

If even....f(-x)   = f(x)

 

f(-x)   =  -3(-x)^4  + 7(-x)^2    =   -3(x)^4 + 7(x)^2   which is true

 

To show that it is odd, we must have that   -f(x)  =   f(x)  .....so....

 

-f(x)  =   -  [ -3x^4 + 7x^2  ]  =  3x^4  - 7x^2   ....not equal to f(x)

 

Thus...it is even

 

P.S.     Even functions are symmetric about the y axis

 

Look at the graph, here :   https://www.desmos.com/calculator/uooawffq1f

 

 

 

cool cool cool

 Feb 6, 2018

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