You can easily see that
[tex] f(x) = g(x)-5 [/tex]
In fact, you have
[tex] g(x)-5 = 2x+3-5 = 2x-2 = f(x) [/tex]
This kind of transformation, where you add a constant to change
[tex] f(x) \mapsto f(x)+k [/tex]
result in a vertical translation, k units up if [tex] k>0 [/tex], k units down if [tex] k<0 [/tex]
So, in this case, the graphs of f(x) and g(x) have the same shape, and they are vertically shifted 5 units apart, g(x) is higher and f(x) is lower.
