1. A strictly monotonic function is defined as a function that either always increases or always decreases in its domain. Suppose we consider all strictly monotonic functions that have (-0, ) as their domain. Explain intuitively why it is true that for all such functions, there is no point in the domain where the tangent line is horizontal. Now recall a specific class of functions called one-one functions. These are functions that have exactly one input corresponding to every output. Explain intuitively why the exact same conclusion about tangent lines can be made for one-one functions as well. Is this enough to say that a strictly monotonic function is always one-one and vice- versa? Discuss.

1. A strictly monotonic function is defined as a function that either always increases or always decreases in its domain. Suppose we consider all strictly monotonic functions that have (-0, ) as their domain. Explain intuitively why it is true that for all such functions, there is no point in the domain where the tangent line is horizontal. Now recall a specific class of functions called one-one functions. These are functions that have exactly one input corresponding to every output. Explain intuitively why the exact same conclusion about tangent lines can be made for one-one functions as well. Is this enough to say that a strictly monotonic function is always one-one and vice- versa? Discuss.

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section: Chapter Questions

Problem 30P: In this problem you are asked to find a function that models in real life situation and then use the...

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1. A strictly monotonic function is defined as a function that either always increases or
always decreases in its domain. Suppose we consider all strictly monotonic functions
that have (-, 0) as their domain. Explain intuitively why it is true that for all such
functions, there is no point in the domain where the tangent line is horizontal. Now
recall a specific class of functions called one-one functions. These are functions that
have exactly one input corresponding to every output. Explain intuitively why the
exact same conclusion about tangent lines can be made for one-one functions as well.
Is this enough to say that a strictly monotonic function is always one-one and vice-
versa? Discuss.

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