Question

Find g(x), where g(x) is the translation 5 units right and 12 units up of f(x)=3x+5.

Answer 1

$f(x)=3x+5\\\downarrow/5\ units\ right/\\f(x-5)=3(x-5)+5\\\downarrow/12\ units\ up/\\f(x-5)+12=3(x-5)+5+12\\\\g(x)=3(x-5)+17=3x-15+17=3x+2\\\\Answer:\ \boxed{g(x)=3x+2}$


Look at the picture.