Mathematicians I. Perepelitsa and C. Douglas are having an argument. Professor Douglas claims that it is impossible for a

Question

Mathematicians I. Perepelitsa and C. Douglas are having an argument. Professor Douglas claims that it is impossible for a function y = f(x) to have the following properties:
a) f(x) is continuous on [-4,4)
b) f(-4)= -2 and f(4) = 2
c) The Intermediate Value Theorem fails in that f(x) = -1 for any input r in [-4,4].
"If f(x) is continuous, then it has to achieve every intermediate value!" screams Professor Douglas. "No," responds Professor
Perepelitsa. "The Intermediate Value Theorem may not apply to this function. I think it is possible for conditions a)-c) to hold."
Who is correct, Professor Douglas or Professor Perepelitsa? If you think Professor Douglas is correct, explain why 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(x) with the stated properties.

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