Question 144117
I certainly hope your book did not tell you the answer is b.


Think about it:  In the second definition of the function, you would have to put an x value that is 2 less than the x value that would give you the same function value in the first definition.


For example:  For R(x) = 0, x = {{{sqrt(7)}}} or {{{-sqrt(7)}}}, but for R(x+2) = 0, x = {{{-2+sqrt(7)}}} or {{{-2-sqrt(7)}}}.


Everything shifts 2 units to the right.  Answer c.


See below:  The green graph is {{{R(x+2)}}}


{{{drawing(600,600,-8,8,-8,8,
grid(1),
graph(600,600,-8,8,-8,8,(x^2-7)/(x^2+1),((x+2)^2-7)/((x+2)^2+1)))}}}