Answer
(a): $Domain (f)= [4,8], Range (f)=[5,9]$
(b): $Domain (f)= [1,5], Range (f)=[2,6]$
(c): $Domain (f)= [4,8], Range (f)=[2,6]$
(d): $Domain (f)= [4,8], Range (f)=[6,18]$
Work Step by Step
The domain of any function consists of the values it can take on the x-axis, whereas the range consists of the values it can take on the y-axis. Here, we apply the given transformation to see how the domain and range have changed:
(a): $Domain (f)= [4,8], Range (f)=[5,9]$ where the graph is shifted upward a distance of 3 units.
(b): $Domain (f)= [1,5], Range (f)=[2,6]$ where the graph is shifted left a distance of 3 units.
(c): $Domain (f)= [4,8], Range (f)=[2,6]$ where the graph is only compressed horizontally by the factor 3.
(d): $Domain (f)= [4,8], Range (f)=[6,18]$ where the graph is stretched vertically by the factor 3.
