Mathematicians B. Constante and M. Sosa are having an argument. Professor Sosa claims that it is impossible for a function y = f(z) to have the following properties: a) f(z) is continuous on [-4, 4) b) f(-4) = 2 and f(4) = –1 c) The Intermediate Value Theorem fails in that f(z) # 1 for any input z in (-4, 4]. "If f(x) is continuous, then it has to achieve every intermediate value!" exclaims Professor Sosa. "No," responds Professor Constante. "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 Sosa or Professor Constante? If you think Professor Sosa is correct, explain why in the space below the image. If you think Professor Constante is correct, use the image below to draw a graph of a function y = f(z) with the stated properties.

Mathematicians B. Constante and M. Sosa are having an argument. Professor Sosa claims that it is impossible for a function y = f(z) to have the following properties: a) f(z) is continuous on [-4, 4) b) f(-4) = 2 and f(4) = –1 c) The Intermediate Value Theorem fails in that f(z) # 1 for any input z in (-4, 4]. "If f(x) is continuous, then it has to achieve every intermediate value!" exclaims Professor Sosa. "No," responds Professor Constante. "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 Sosa or Professor Constante? If you think Professor Sosa is correct, explain why in the space below the image. If you think Professor Constante is correct, use the image below to draw a graph of a function y = f(z) with the stated properties.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

Mathematicians B. Constante and M. Sosa are having an argument. Professor Sosa 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) = -1
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!" exclaims Professor Sosa. “No," responds Professor
Constante. "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 Sosa or Professor Constante? If you think Professor Sosa is correct, explain why in the space below
the image. If you think Professor Constante is correct, use the image below to draw a graph of a function y = f() with the
stated properties.

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