Please show work needed. Thank you

4. [9 points} Mathematicians I. Perepelitsa and C. Douglas are having an argument. Professor Douglas claims that it is imth for a function y = flier] to have the following properties: a} fin} is continuous on [41 4] h} .H_4j = 2 and fill] = 2 c} The Intermediate Value Theorem fails in that x} 9'5 1 for any input :I.' in [4.4]. \"If n] is continuous, then it has to achieve ever},r intermediate 1value!\" screams Professor Douglas. \"No," responds Professor Perep-elitsa. \"The Intermediate Value Theorem may not apply to this function. I think it is possible for conditions aj-c} to hold.\" 1Who is correct, Professor Douglas or Professor P'erepelitsa? If you think Professor Douglas is correct, explain whr in the space below the image. If you think Professor Perepelitsa is correct. use the image below to draw a graph of a function y = f{:} with the stated properties