Question

Without graphing, what is the transformation that takes place between the graph `y=1/x` and the graph of `y=1/(x+5)-2`?

Answer 1

The graph of `g` is the graph of `1/x`, shifted `5` units to the left, and `2` units down.

Explanation:

Let `f(x) = 1/x`, and `g(x) = 1/(x+5) - 2`. Then,

`g(x) = f(x+ 5) - 2`.

Therefore, the graph of `g` is the graph of `f`, shifted `5` units to the left, and `2` units down.

In general, for any two functions `f,g`, if `g(x) = f(x - a) + b`, then

the graph of `g` is the graph of `f` shifted `a` units to the right, and `b` units upwards. Negative values mean opposite directions.