Question

Determine if the following function has symmetry with respect to the y-axis or origin.y=1/xSymmetrical with respect to the originNo SymmetrySymmetrical with respect to the x-axisSymmetric with respect to the y-axis

Answer 1

Step 1

Given; Determine if the following function has symmetry with respect to the y-axis or origin. y=1/x

Symmetrical with respect to the origin

No Symmetry

Symmetrical with respect to the x-axis

Symmetric with respect to the y-axis

Step 2

`\begin{gathered} y=(1)/(x) \\ x-axis\text{ test} \\ -y=(1)/(x) \\ The\text{ x-axis tes t failed} \end{gathered}`
`\begin{gathered} y=(1)/(x) \\ y-axis\text{ test} \\ y=(1)/(-x) \\ y-axis\text{ test failed} \end{gathered}`
`\begin{gathered} origin\text{ test} \\ -y=(1)/(-x) \\ cross\text{ multiply} \\ xy=1 \\ solve\text{ back for y} \\ y=(1)/(x) \\ Hence,\text{ the symmetry is with respect to the origin} \end{gathered}`

Answer;

`Symmetrical\text{ with respect to the origin}`