Question

name date - tests for symmetry hw 2. ( xy=-4 ) x - axis y - axis origin none

Explanation:

Step1: Test for x - axis symmetry

Replace \(y\) with \(-y\). If \(xy=- 4\) becomes \(x(-y)=-4\) or \(xy = 4\) which is not the same as the original equation \(xy=-4\), so it is not symmetric about the \(x\) - axis.

Step2: Test for y - axis symmetry

Replace \(x\) with \(-x\). If \(xy=-4\) becomes \((-x)y=-4\) or \(xy = 4\) which is not the same as the original equation \(xy=-4\), so it is not symmetric about the \(y\) - axis.

Step3: Test for origin symmetry

Replace \(x\) with \(-x\) and \(y\) with \(-y\). \((-x)(-y)=-4\) simplifies to \(xy=-4\), which is the same as the original equation.

Answer:

origin