Question

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Answer 1

The equation of the graph y= $x^{3}-2x^{2} +3x-4$ has no symmetry

The equation of the graph y = $x^{3}-2x^{2} +3x-4$

Replace y with -y in the given equation

-y = $x^{3}-2x^{2} +3x-4$

When replacing y with -y gives the different equation. The equation is not symmetric with respect to x axis

Replace x with -x in the given equation

y = $(-x)^{3} -2(-x^{2} )-3(-x)-4$

y = $-x^{3}-2x^{2} +3x-4$

When replacing x with -x gives the different equation. The equation is not symmetric with respect to y axis

Replace x with -x and y with -y in the equation

-y = $(-x)^{3} -2(-x^{2} )-3(-x)-4$

-y =  $-x^{3}-2x^{2} +3x-4$

When replacing x with -x and y with -y gives the different equation. The equation is not symmetry with respect to origin.

Hence, the equation of the graph y= $x^{3}-2x^{2} +3x-4$ has no symmetry

Learn more about symmetry here

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