Question

PLEASE HELP!!!

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 left and 3 units up.
B. The graph shifts 3 units right and 5 units down.
C. The graph shifts 5 units right and 3 units down.
D. The graph shifts 3 units left and 5 units up.

Answer 1

A) The graph shifts 5 units left and 3 units up.

Explanation:

For a function
`f(x)` following transformation rules is applied.

`f(x-c)\rightarrow` shifts function
`c` units to the right.

`f(x+c)\rightarrow` shifts function
`c` units to the right.

`f(x)+b\rightarrow` shifts function
`c` units upward.

`f(x)-b\rightarrow` shifts function
`c` units down upward.

Given function
`f(x)`:

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

Function
`g(x)`:

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

So, to transform
`f(x)` to
`g(x)` we can make changes as

`f(x)=(1)/(x-4+(5))+3+(3)=(1)/(x+1)+6=g(x)`

Comparing the two function we conclude the following transformation taking place:

`g(x)=f(x+5)+3`

From the above rule stated, we can make a statement about the transformation as following:

The graph shifts 5 units left and 3 units up.