Think about the transformations that have to be taken from the function f(x) to get f(5x + 3) and 5f(x) + 3. The first has a dilation of factor 1/5 in the x direction and a translation of 3 units left, while the second has a dilation of factor 5 in the y direction and a translation of 3 units up.
How do these transformations affect the domain and range of the original function?
March 16th 2013, 09:19 PM
Re: Domain and Range
For the function f(5x+3) will have the same domain as well as range.
In the second case let the function be g(x) = 5 f(x) + 3 .
Its domain will depend on the range is whatsoever is the range of f(x) i.e., [4,10] and range will be [ 5*4+3, 5*10+3] i.e., [23, 53]