The function \( P(n) \) has a domian of \( -3 \leq n \leq 8 \) and a range of \( -6 \leq P(n) \leq 12 \). Express a new function \( R(n) \) in terms of \( P(n) \) that would have a domain of \( -3 \leq n \leq 8 \) and a range of \( -60 \leq R(n) \leq 30 \).

5th Ed: #25

The diameter of the range of \( P(n) \) is \(12+6 = 18 \) and the diamter of the range of \( R(n) \) is \( 30+60 = 90 \), Since the diameter of \(R(n) \) is 5 times that of \( P(n) \), first we can take \( 5P(n) \).
But \(5P(n) \) has a range of \( -30 \leq 5P(n) \leq 60 \), so we would then need to shift down 30, giving us \( R(n) = 5P(n) - 30 \)