Given the functions f(x)=1x−4+3 and g(x)=1x+1+6 . Which statement describes the transformation of the graph of function f onto the graph of function g?

Question

 The graph shifts 3 units left and 5 units up.

The graph shifts 3 units right and 5 units down.

The graph shifts 5 units left and 3 units up.

The graph shifts 5 units right and 3 units down.

Answer 1

If you simplify the functions

 

f(x)=1x-1

g(x)=1x+7

 

Both functions have a slope of +1.  The y-intercept of f(x) is -1 and of g(x) is 7.  The x-intercept of f(x) is 1 and of g(x) is -7.  Since f(x) is located below and to the right of g(x) by 8 units, it must be shifted left a units and up b units such that a+b=8 in order to match g(x).

So the first and third answer choices are both correct.