Mathfunctions
posted by Alana K
A function, y = f(x), originally has a domain of x equal or bigger than 4 and a range of y equal or smaller than 1. Determine the new domain and range of y=2f(x+5)+1 after applying all transformations. (Hint: Sketch the graph&apply the transformations)
Note: I have tried many approaches to this and I am stuck. How do I solve this if I don't know what the original equation is?

Steve
If the domain of f(x) is x > 4
then the domain of f(x+5) is
x+5 > 4
x < 1
The range of f(x) is y <= 1
The range of 2f(x) is y >= 2
The range of 2f(x)+5 is y >= 2+5 or y >= 3
Consider f(x)=x^2+1
2f(x)+5 = 2x^2+3
Using f(x+5) does not affect the range  it just shifts/reflects horizontally 
Alana K
Thank you for response Steve. How did you get 2f(x) is y >= 2 ? I keep thinking it should be 1/2

Alana K
never mind, ignore my last comment, it's incorrect. thank you for your help.
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