Given the functions f(x)=1x−2+1 and g(x)=1x+5+9 .

which statement describes the transformation of the graph of function f onto the graph of function g?

the graph shifts 8 units left and 7 units up.

the graph shifts 8 units right and 7 units down.

the graph shifts 7 units left and 8 units up.

the graph shifts 7 units right and 8 units down.

For this problem you would look at the difference between the two equations. Left and right is determined by the -2 and the +5 in the problems, to get from -2 to +5, you would add 7 but (and i dont really know how to explain the reasoning for this) whenever this number is positive, it goes left and whenever it is negative, it goes right. Figuring out if it shifts up or down is the same, look at the numbers +1 and +9 in the equations. If you go from +1 to +9, you would be adding 8, and this makes it shift upward.

Therefore the answer is the third one: the graph shifts 7 units left and 8 units up