2. [5 pts] Consider the function : R 0 R, 9 (x) = x+ (a)...

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2. [5 pts] Consider the function : R \ 0 R, 9 (x) = x+ (a) [1 pt] Draw the graph of f. (b) [2 pts] Let A = [3,0], B = (0,). Prove that f(x) : A B is injective by two different methods i. [1 pt] Using the definition of injectivity. ii. [1 pt] Constructing a left inverse. (c) [2 pts] Let A2 = (0, 00], B = [6,00). Prove that f(x): A2B is surjective by two different methods i. [1 pt] Using the definition of surjectivity. ii. [1 pt] Constructing a right inverse. 3. [2 pts] For each of the following statements, determine if they are true or false, by either provide a proof or giving a counter example. (a) [1 pt] Any surjective function : R R is unbounded. (b) [1 pt] Every unbounded function : R R is surjective. 2. [5 pts] Consider the function : R \ 0 R, 9 (x) = x+ (a) [1 pt] Draw the graph of f. (b) [2 pts] Let A = [3,0], B = (0,). Prove that f(x) : A B is injective by two different methods i. [1 pt] Using the definition of injectivity. ii. [1 pt] Constructing a left inverse. (c) [2 pts] Let A2 = (0, 00], B = [6,00). Prove that f(x): A2B is surjective by two different methods i. [1 pt] Using the definition of surjectivity. ii. [1 pt] Constructing a right inverse. 3. [2 pts] For each of the following statements, determine if they are true or false, by either provide a proof or giving a counter example. (a) [1 pt] Any surjective function : R R is unbounded. (b) [1 pt] Every unbounded function : R R is surjective.