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?
a- the graph shifts 5 units right and 3 units down
b- the graph shifts 5 units left and 3 units up
c- the graph shifts 3 units right and 5 units down
d- the graph shifts 3 units left and 5 units up.

Option B.

Step-by-step explanation:

The first transformation we can apply is to do:

F(x) +3

As

So

.

This operation moves the function upwards by 3 units.

The second transformation is to make F(x + 5)

This transformation moves the function 5 units to the left.

Note that now

The results of these transformations was an upward displacement of 3 units and one to the left of 5 units.

Finally the answer is option B

B- the graph shifts 5 units left and 3 units up