Use the graph of
For the reciprocal function,
Sketch the vertical asymptotes.
Upward parabola, vertex at (0, comma negative 4), x intercepts at negative 2 & 2, dashed vertical segments at x = negative 2 and x = 2.
Mark the places where
Added approximate highlighted points on parabola, (negative 2.2, comma 1), (2.2, comma 1), (negative 1.7, comma negative 1), & (1.7, comma negative 1).
The reciprocal at the point
Draw a smooth curve from it to where
Added, downward curve between highlighted points below x axis, going through the point (0, comma 1 fourth).
Added, 4 almost vertical curves, from each of the highlighted points above x axis, to infinity, and from each of the highlighted points below the x axis, to negative infinity.
Added, upward curves from approximate point, (negative 2.2, comma 1), going left above x axis, from approximate point (2.2, comma 1), going right above x axis.