Math 1151, Summer 2023 Written Homework 1 Page 2 of 6 Problem 1: Graphing a Function (18 points) Sketch the graph of a function f satisfying all of the following properties. a) (2 points) 1' is an odd function with domain [76, 6]. b) (3 points) 1' has intervals of continuity: [76,74), [74,72), (72,0), (0,2), (24], and (4, 6]. c) (3 points) f(0) : O, {(4) : 0 and {(6) : 3. ( ) cl) 3 points lim f(x) : 4 and lim {(x) : 1 x~>04r 14)? e) (1 point) Iim f(x) : *2. x>4+ f) (3 points) f(x) > 0 for x in (0, 2) U (2,4) U (5,6), g) (3 points) f(x) 2 a) (3 points) Evaluate |irr21 k(x). Cite any limit laws you use. xe t J32. W) : Page 5 of 6 b) (6 points) Evaluate lim k(x). In this part individual limit laws do not need to be cited, but you must check the form x42- and show your work. Form: Iim k(x) : x%2 c) (3 points) Is k(x) continuous at x : 2? Is it left-continuous? Is it right-continuous? Make sure you answer all three questions. and justify your answers using the definition of continuity. Math 1151, Summer 2023 Written Homework 1 Page 6 of 6 cl) (2 points) Explain why k(x) is continuous for any value of x 2. [HINTz If x > 2, what is k(x)?] f) (2 points) Use your previous work to write the intervals of continuity for k(x). No justification is required for this part, but your answer should be consistent with your previous work