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Determine whether the graph of the given function f(x) = 4x^3 is symmetric with respect to the y-axis, symmetric with respect to the origin, or neither.

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2 Answers

f(x) = 4x^3
 
f(-x) = 4(-x)^3 = -4x^3 = -f(x)
 
So the f is symmetric with respect to the origin and "odd".
 
But f(-x) ≠ f(x) so f is not symmetric with respect to the y-axis so is not "even".
 
[N.B.: Any circle x^2 + y^2 = r^2 is symmetric to any line through the origin: it's even, odd, and its own inverse.]
 f(x ) = 4X^3
 
 
   f( 1) = 4 ( 1 ) ^3 = 4
 
   f ( -1 ) = 4 (-1)^3 = -4 
 
  It is not Symmetric with respect to Y- axis : Because f(1) ≠ f( -1)
 
   It is Symmetric w.r.t origin because  :   f( 1) = - f( -1)