Find the domain and range of the following: 1/3f(x-3)

Question

Let the domain of f(x) be [-1,2] and the range be [0,3].

Answer 1

Replacing x by x-3 translates the graph of y=f(x) three units to the right, hence the domain of y = f(x) gets translated three units to the right.  

 

Multiplying a function by 1/3 multiplies all the range elements of           y = f(x) by 1/3.

 

Domain of y = (1/3)f(x-3) :  [2,5]

 

Range of y = (1/3)f(x-3) :    [0,1]