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

Answer:

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

Step-by-step 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 $f(x)$:

$f(x)=\frac{1}{x-4}+3$

Function  $g(x)$:

$g(x)=\frac{1}{x+1}+6$

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

$f(x)=\frac{1}{x-4+(5)}+3+(3)=\frac{1}{x+1}+6=g(x)$

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.