1. Let f (0, ∞)→ R be the function with f(x) = |1 ln x]. Sketch the graph of y = f(x). Give a brief justification (one sentence each) why f is not injective and why f is not surjective. Come up with a subset A of R of your choice such that the function g: A → R with g(x) = 1 In x is injective. No justification needed. Come up with a subset B of R of your choice such that the function h: (0, ∞) → B with h(x) = 1- ln x is surjective. No justification needed.

Suppose f is a function with f(2)=5 where for all interval > 0, there is some δ > 0 such that if x interval (2-δ, 2) U (2, 2+δ ), then f(x) interval (3-ε, 3+ε). Sketch a possible graph of f.

For each one, classify it as Injective but not surjective, Surjective but not injective, Neither injective nor surjective, or Bijective. If a function does have a property you do not have to explain why; but if a function fails to have a property, you should explain why in as specific of terms as possible.  f:Z→Z given by f(a)=2a g:N→N  given by g(a)=a2−1 The mapping h from the set of all lists of integers (such as [7,3,-2,10]) to Z that takes the list and returns the sum of the elements in the list. For example h([7,3,−2,10])=18

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