Graph$y=\frac{1}{x}$

The given equation is

$y=\frac{1}{x}$

For x-intercepts, take $y=0$

$$\begin{gathered} y=\frac{1}{x} \\ 0=\frac{1}{x} \end{gathered}$$

solution of x is not possible so there are no x-intercepts

For y-intercepts, take $x=0$

$$\begin{gathered} y=\frac{1}{x} \\ y=\frac{1}{0} \end{gathered}$$

solution ofyis undefined so there are noy-intercepts.

To check the symmetry with respect to the x-axis, substitute$-y$for $y$in the equation

$$\begin{gathered} -y=\frac{1}{x} \\ y=-\frac{1}{x} \end{gathered}$$

the equation is not equivalent to the original equation

so the graph of the equation is not symmetric with respect to x-axis

To check the symmetry with respect to the y-axis, substitute$-x$ for x in the equation

$$\begin{gathered} y=\frac{1}{-x} \\ y=-\frac{1}{x} \end{gathered}$$

the equation is not equivalent to the original equation

so the graph of the equation is not symmetric with respect to y-axis

To check the symmetry with respect to the y-axisand x-axis, substitute$-x$ for x and$-y$ for yin the equation

$$\begin{gathered} -y=\frac{1}{-x} \\ y=\frac{1}{x} \end{gathered}$$

the equation is equivalent to the original equation

so the graph of the equation is symmetric with respect to the origin

Consider the different values of x and determine coordinates of several points

Plot the points and connect them by the smooth curve