Question

Given the functions f(x)= 1/x−4 +3 and g(x)=1/x+1 +6 .

Which statement describes the transformation of the graph of function f onto the graph of function g?



The graph shifts 5 units right and 3 units down.


The graph shifts 3 units left and 5 units up.


The graph shifts 5 units left and 3 units up.


The graph shifts 3 units right and 5 units down.

Answer 1

The graph shifts 5 units left and 3 units up.

Step-by-step explanation

The given functions are:

`f(x) = (1)/(x - 4) + 3`

and

`g(x) = (1)/(x + 1) + 6`

We want to transform f(x) so that, it coincide with the g(x).

The required transformation is

`f(x+5)+3`

Let us see why this works.

`f(x+5)+3 = (1)/(x + 5- 4) + 3 + 3`

`f(x+5)+3 = (1)/(x + 1) + 6 = g(x)`

The transformation f(x+5)+3 will shift f(x) 5 units left and 3 units up.

The third choice is correct.