Question

Given the functions

Answer 1

Answer:

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

Step-by-step explanation:

The function F(x) = 1/x-4 + 3 can be transformed to G (x) = 1/x+1 + 6,

The transformation can be determined by comparing the two functions;

Such that;  (1/x+1 + 6) -  (1/x-4 + 3) we get; +5 , +3

Which means; the function F(x) = 1/x-4 + 3 can be transformed to G (x) = 1/x+1 + 6; by shifting the graph 5 units left and 3 units up, since 5 is positive (left) and 3 is positive (up).

Answer 2

Answer:

Option B.

Step-by-step explanation:

The first transformation we can apply is to do:

F(x) +3

As

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

So

$F(x) +3 = \frac{1}{x-4} + 6$.

This operation moves the function upwards by 3 units.

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

$F(x+5) = \frac{1}{(x+5)-4} + 6\\\\F(x+5) = \frac{1}{(x+1)} + 6$

This transformation moves the function 5 units to the left.

Note that now $F(x + 5) +3 = G(x).$

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