Question

Given the functions f(x)= rac{1}{x-2} + 1 " alt=" \frac{1}{x-2} + 1 " align="absmiddle" class="latex-formula"> and g(x) = $\frac{1}{x+5} + 9$
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.