is there any way to check the following function for x and y axis symmetry without graphing??
g(x)=(1/X^2))+(5/x)+6
Let [tex]F(x,y)=0[\math] be a curve. Then it is x-axis symmetry iff $\displaystyle F(x,y)=0\leftrightarrow F(x,-y)=0$. It is y-axis symmetry iff$\displaystyle F(x,y)=0\leftrightarrow F(-x,y)=0$
In this specific problem, you only have to check whether $\displaystyle g(x)=g(-x)$ to judge whether it is y-axis symmetry. It is clearly impossible that it is x-axis symmetry because it is written in the form$\displaystyle y=g(x)$(except$\displaystyle g(x)\equiv 0$)