Question

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

Answer 1

ANSWER

The graph shifts 5 units left and 3 units up.

EXPLANATION

The given functions are:

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

and

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

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.

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

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

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

The third choice is correct.

Answer 2

Answer with step-by-step explanation:

We are given a function $f(x) = \frac{1}{x - 4} + 3$ which is to be transformed to another function $g(x) = \frac{1}{x + 1} + 6$.

We are to determine whether which statement describes the transformation of the graph of function f onto the graph of function g.

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

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

$f(x)=g(x)$

Therefore, the correct answer option is: The graph shifts 5 units right and 3 units up.