Question

How do graphs of y = 1/x and y = 5/x+6 compare?

Answer 1

The graph of y = 5/(x + 6) is a vertical stretching of y = 1/x by a factor of 5 and a horizontal translation to the left by 6 units.

A function y = kf(x) is a vertical stretch of y = f(x), if:

`k\gt1`

y = kf(x) is a vertical compression of y = f(x), if:

`0\lt k\lt1`

A function f(x + k) is a horizontal translation to the left of f(x), if:

`k\gt0`

f(x + k) is a horizontal translation to the right of f(x), if:

`k\lt0`