Can someone tell me how to solve "With respect to which of the following is the graph of y =2X3 (X to the power of 3) - 5x symmetric?"

Question

anonymous · Answer

it is hard to sketch the cubic equation, I guess if you wanna find the symmetric equation of this function and if it is multiple choice, you could plug in some points or use some tricks to figure out the answer.

anonymous · Answer

Since the powers are odd ( 3 and 1), it's symmetric. Since f(-x)=- f(x). Hence it's symmetric around the origin. If you have difficulty imaging plot f(-x) = -f(x)

dumbcow · Answer

i agree
if you want to check if its symmetric about the y-axis
f(-x) = f(x)
this is true for even powers

anonymous · Answer

$$y=2x^3-5x$$ symmetric with respect to the origin (0,0) which means if you fold your paper in half twice, along the x - axis and then the y - axis the graph will be the same.  it also means that if 
$$(a,b)$$ ins on the graph so is 
$$(-a,-b)$$