absolute value - vertical shift up 5, horizontal shift right 3

Question

write the equation of the transformed function f(x) and give the domain and range of the function 

Answer 1

f(x)=|x-3|+5

 

Remember that:

f(x-h) shifts the graph to the right horizontally

f(x+h) shifts the graph to the left horizontally

f(x)+k shifts the graph up vertically, because your outputs increase

f(x)-k shifts the graph down vertically, because your outputs are decreased.

 

So the rule applied to the absolute value function is f(x-3)+5, where f(x)=|x|.