Question 1086965
{{{f(x) = -x^3(x + 2)^2(x - 6)}}}


the graph will be symmetrical with respect to the y-axis if:

{{{f(-x) = f(x)}}}

check: 

{{{f(-x) = f(x)}}}......if {{{x=1}}}

{{{f(-1) = f(1)}}}

{{{ (-(-1)^3)(-1 + 2)^2(-1-6)=-1^3(1 + 2)^2(1-6)}}}

{{{ -(-1)(1)^2(-7)=-1(3)^2( -5)}}}

{{{ 1(1)(-7)=-1(9)( - 5)}}}

{{{ -7<>45}}}=>the graph is {{{not}}} symmetrical with respect to the y-axis



the graph will be symmetrical with respect to the origin if:



{{{f(-x) = -f(x)}}}......if {{{x=1}}}

{{{f(-1) = f(1)}}}

{{{ -(-1)^3(-1 + 2)^2(-1 - 6)=-1^3(1 + 2)^2(1 - 6)}}}

{{{ -(-1)(1)^2(-7)=-(-1(3)^2( - 5))}}}

{{{ 1(1)(-7)=-(-1(9)( - 5))}}}

{{{ -7<>-45}}}=>the graph is {{{not}}} symmetrical with respect to the origin


{{{ graph( 600, 600, -20, 20, -20, 20, -x^3(x + 2)^2*(x - 6),-x^6+2x^5+20x^4+ 24x^3) }}}


answer: {{{neither}}}