SOLUTION: Y=-6x^3+7x symmetric with the y axis, the x axis or the origin?

Algebra ->  Graphs -> SOLUTION: Y=-6x^3+7x symmetric with the y axis, the x axis or the origin?      Log On


   

Question 1064134: Y=-6x^3+7x symmetric with the y axis, the x axis or the origin?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The equation Y=-8x%5E3%2B7x assigns one and only one Y value to each x value.
It determines Y as a function of x.
It cannot have the same x associated with Y and with -Y for all values of Y,
so the graph cannot be synnetrical with respect to the x-axis.
Y%28x%29=-6x%5E3%2B7x so -Y%28x%29=6x%5E3-7x .
Y%28-x%29=-6%28-x%29%5E3%2B7%28-x%29=-6%28-x%5E3%29-7x=6x%5E3-7x .
Since Y%28-x%29=-Y%28x%29 ,
the function is symmetrical with respect to the origin.