Question

If G(x)=1/x were shifted 4 units to the left and 4 units up, what would the new equation be?

Answer 1

`f(x) = 1/(x+4)+4`

Explanation:

Given:

`g(x) = 1/x`

graph{1/x [-10, 10, -5, 5]}

If we want our new function to be like `g(x)` but shifted left `4` units, then we need to put `x+4` in place of `x`. That way, when you put `-4` into the new function then the result is the same as putting `0` into the old - i.e. an undefined result since that's where `1/x` has its vertical asymptote.

To move our new function up `4` units, simply add `4`.

So our transformed function is:

`f(x) = 1/(x+4)+4`

graph{1/(x+4)+4 [-12.125, 7.875, -2.28, 7.72]}