Question

Given the functions f(x)=
`(1)/(x-2) + 1` and g(x) = 
`(1)/(x+5) + 9`

Which statement describes the transformation of the graph of function f onto the graph of function g?
The graph shifts 8 units right and 7 units down.

The graph shifts 8 units left and 7 units up.

The graph shifts 7 units right and 8 units down.

The graph shifts 7 units left and 8 units up.

Answer 1

f (x) = (1 / (x-2)) + 1g (x) = (1 / (x + 5)) + 9
Transformation of functions:
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
To graph y = f (x) -k, move the graph of k units down.
Suppose that h> 0
To graph y = f (x-h), move the graph of h units to the right.
To graph y = f (x + h), move the graph of h units to the left.

f (x) = (1 / (x-2)) + 1
To graph y = f (x) + k, move the graph of k units up.
h (x) = (1 / (x-2)) + 1 + 8
To graph y = f (x + h), move the graph of h units to the left.
g (x) = (1 / (x-2 + 7)) + 1 + 8
g (x) = (1 / (x + 5)) + 9

Answer:
The graph shifts 7 units left and 8 units up.