What effect does "a" have on the parent function y=1/x

Y=1/x is a reciprocal function & its shape is a special hyperbola with one branch located in the 1st Quadrant and the second in the 3dr Quadrant and both are symmetric about the origin O.

If a> 1 → y=a/x and the 2 branches are equally stretched upward & downward

about the center O.

If 0 < a < 1→y = a/x, the 2 branches are equally stretched downward and upward about the center O.

If a<0, then the 2 legs are in the 2nd and 4th Quadrant respectively