Question

Graph the following with the indicated transformation. Please show any calculations necessary to arrive at your graph and write the equation of the new graph.f(x)=√ x
shifted 4 units up

Answer 1

The important thing to remember is that given a function f(x), then \[f(x)+a\] will always be a shift in the vertical direction, with the shift being UP if a is POSITIVE and the shift being DOWN if a is NEGATIVE. Similarly, \[f(x-a)\] is a shift in the horizontal direction, with the shift to the RIGHT if a is POSITIVE and the shift being LEFT if a is NEGATIVE. Thus, shifting f(x) = sqrt(x) 4 units up would just be \[g(x)=\sqrt{x}+4\] And of course you can graph it using whatever method you prefer.