Question

How are the graphs `f(x)=1/x` and `g(x)=3/x` related?

Answer 1

See explanation below

Explanation:

The given functions:

`f(x)=1/x`

`g(x)=3/x`

Both the above functions represent two rectangular hyperbolas which are symmetrical about origin.

Both the branches of these hyperbolas are parallel to each other in I & III quadrants. The vertical distance between any two corresponding points on these hyperbolas is

`=3/x-1/x`

`=2/x`

Hence the graph of `3/x` is obtained by vertically shifting the graph of `1/x` by `2/x` units upward in I quadrant & `2/x` units downward in III quadrant.