Question

The graph of xy = 1 is symmetric about

• A. x-axis
• B. y-axis
• C. line y = x
• D. origin

Answer 1

Answer: (C), (D)

origin

$\mathrm{xy}=1\Rightarrow y=\frac{1}{x}\mathrm{Let}f\left(x\right)=\frac{1}{x}\mathrm{then}f\left(-x\right)=-\frac{1}{x}=-f\left(x\right)$
Therefore, the given function is odd.
We know that if f(x) is an odd function, then graph of equation y = f(x) is symmetric about the origin.

Also, a graph is symmetric about the line y = x, if equation remains same after replacing x with y and y with x in the equation. Hence, it is also symmetric with the line y=x.
Hence, its graph is symmetric about the origin
and the line y = x.