Determine whether the graph of the given function is symmetr

Determine whether the graph of the given function is symmetric with respect to the y-axis, symmetric with respect to the origin, or neither Use standard window to support your conclusion, f(x) 0.6x Choose the correct answer below O A. The graph of the function foxy o 2x xis neither symmetric with respect to the origin nor symmetric with respect to the y axis O B. The graph of the function fox) 0.6x -2x x is symmetric with respect to the origin O C. The graph of the function fox) 0,6x +x is symmetric with respec to the y axis

Solution

Given, f(x)=0.6x^7-2x^5+x

Condition for symmetric with respect to y-axis is, y axis is act as a mirror ie, f(x)=f(-x)

Now f(-x)=0.6(-x)^7-2(-x)^5+(-x)=-0.6x^7+2x^5-x=-f(x)

hence function is not symmetric about y-axis

Now Condition for symmetry with origin

reflection in the x axis, follwed by reflection in the y axis

here f(x)=-f(x) hence function is symmetry about origin

Hence (B) is correct.