You have given a function λ : R → R with the following properties (x ∈ R, n ∈ N): λ(n) = 0 , λ(x + 1) = λ(x) , λ
n +
1
2

= 1
Find two functions p, q : R → R with q(x) 6= 0 for all x such that λ(x) = q(x)(p(x) + 1).

Charlie is at an amusement park that has 18 different rides. each ride costs $1.75. the function c(r) = 1.75r represents the total amount of money that charlie will spend if he goes on r rides, but he never goes on the same one more than once. what domain and range are reasonable for the function?